ceph/src/boost/libs/math/reporting/performance/fibonacci.hpp

   1 #pragma once
   2
   3 #include <vector>
   4 #include <boost/multiprecision/cpp_int.hpp>
   5 #include <boost/lexical_cast.hpp>
   6
   7 template <class T>
   8 std::vector<T> const& fibonacci_numbers(const boost::mpl::int_<16>&)
   9 {
  10    static const boost::uint16_t numbers[] = {
  11       static_cast<boost::uint16_t>(21u),
  12       static_cast<boost::uint16_t>(34u),
  13       static_cast<boost::uint16_t>(55u),
  14       static_cast<boost::uint16_t>(89u),
  15       static_cast<boost::uint16_t>(144u),
  16       static_cast<boost::uint16_t>(233u),
  17       static_cast<boost::uint16_t>(377u),
  18       static_cast<boost::uint16_t>(610u),
  19       static_cast<boost::uint16_t>(987u),
  20       static_cast<boost::uint16_t>(1597u),
  21       static_cast<boost::uint16_t>(2584u),
  22       static_cast<boost::uint16_t>(4181u),
  23       static_cast<boost::uint16_t>(6765u),
  24       static_cast<boost::uint16_t>(17711u),
  25       static_cast<boost::uint16_t>(10946u),
  26       static_cast<boost::uint16_t>(17711u),
  27       static_cast<boost::uint16_t>(28657u),
  28       static_cast<boost::uint16_t>(46368u)
  29    };
  30    static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0]));
  31
  32    return data;
  33 }
  34
  35 template <class T>
  36 std::vector<T> const& fibonacci_numbers(const boost::mpl::int_<32>&)
  37 {
  38    static const boost::uint32_t numbers[] = {
  39       21u,
  40       34u,
  41       55u,
  42       89u,
  43       144u,
  44       233u,
  45       377u,
  46       610u,
  47       987u,
  48       1597u,
  49       2584u,
  50       4181u,
  51       6765u,
  52       10946u,
  53       17711u,
  54       28657u,
  55       46368u,
  56       75025u,
  57       121393u,
  58       196418u,
  59       317811u,
  60       514229u,
  61       832040u,
  62       1346269u,
  63       2178309u,
  64       3524578u,
  65       5702887u,
  66       9227465u,
  67       14930352u,
  68       24157817u,
  69       39088169u,
  70       63245986u,
  71       102334155u,
  72       165580141u,
  73       267914296u,
  74       433494437u,
  75       701408733u,
  76       1134903170u,
  77       1836311903u,
  78       2971215073u
  79    };
  80    static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0]));
  81
  82    return data;
  83 }
  84
  85 template <class T>
  86 std::vector<T> const& fibonacci_numbers(const boost::mpl::int_<64>&)
  87 {
  88    static const boost::uint64_t numbers[] = {
  89       21uLL,
  90       34uLL,
  91       55uLL,
  92       89uLL,
  93       144uLL,
  94       233uLL,
  95       377uLL,
  96       610uLL,
  97       987uLL,
  98       1597uLL,
  99       2584uLL,
 100       4181uLL,
 101       6765uLL,
 102       10946uLL,
 103       17711uLL,
 104       28657uLL,
 105       46368uLL,
 106       75025uLL,
 107       121393uLL,
 108       196418uLL,
 109       317811uLL,
 110       514229uLL,
 111       832040uLL,
 112       1346269uLL,
 113       2178309uLL,
 114       3524578uLL,
 115       5702887uLL,
 116       9227465uLL,
 117       14930352uLL,
 118       24157817uLL,
 119       39088169uLL,
 120       63245986uLL,
 121       102334155uLL,
 122       165580141uLL,
 123       267914296uLL,
 124       433494437uLL,
 125       701408733uLL,
 126       1134903170uLL,
 127       1836311903uLL,
 128       2971215073uLL,
 129       4807526976uLL,
 130       7778742049uLL,
 131       12586269025uLL,
 132       20365011074uLL,
 133       32951280099uLL,
 134       53316291173uLL,
 135       86267571272uLL,
 136       139583862445uLL,
 137       225851433717uLL,
 138       365435296162uLL,
 139       591286729879uLL,
 140       956722026041uLL,
 141       1548008755920uLL,
 142       2504730781961uLL,
 143       4052739537881uLL,
 144       6557470319842uLL,
 145       10610209857723uLL,
 146       17167680177565uLL,
 147       27777890035288uLL,
 148       44945570212853uLL,
 149       72723460248141uLL,
 150       117669030460994uLL,
 151       190392490709135uLL,
 152       308061521170129uLL,
 153       498454011879264uLL,
 154       806515533049393uLL,
 155       1304969544928657uLL,
 156       2111485077978050uLL,
 157       3416454622906707uLL,
 158       5527939700884757uLL,
 159       8944394323791464uLL,
 160       14472334024676221uLL,
 161       23416728348467685uLL,
 162       37889062373143906uLL,
 163       61305790721611591uLL,
 164       99194853094755497uLL,
 165       160500643816367088uLL,
 166       259695496911122585uLL,
 167       420196140727489673uLL,
 168       679891637638612258uLL,
 169       1100087778366101931uLL,
 170       1779979416004714189uLL,
 171       2880067194370816120uLL,
 172       4660046610375530309uLL,
 173       7540113804746346429uLL,
 174       12200160415121876738uLL,
 175    };
 176    static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0]));
 177
 178    return data;
 179 }
 180
 181 template <class T>
 182 std::vector<T> const& fibonacci_numbers(const boost::mpl::int_<0>&)
 183 {
 184    static const T numbers[] = {
 185       boost::lexical_cast<T>("21"),
 186       boost::lexical_cast<T>("34"),
 187       boost::lexical_cast<T>("55"),
 188       boost::lexical_cast<T>("89"),
 189       boost::lexical_cast<T>("144"),
 190       boost::lexical_cast<T>("233"),
 191       boost::lexical_cast<T>("377"),
 192       boost::lexical_cast<T>("610"),
 193       boost::lexical_cast<T>("987"),
 194       boost::lexical_cast<T>("1597"),
 195       boost::lexical_cast<T>("2584"),
 196       boost::lexical_cast<T>("4181"),
 197       boost::lexical_cast<T>("6765"),
 198       boost::lexical_cast<T>("10946"),
 199       boost::lexical_cast<T>("17711"),
 200       boost::lexical_cast<T>("28657"),
 201       boost::lexical_cast<T>("46368"),
 202       boost::lexical_cast<T>("75025"),
 203       boost::lexical_cast<T>("121393"),
 204       boost::lexical_cast<T>("196418"),
 205       boost::lexical_cast<T>("317811"),
 206       boost::lexical_cast<T>("514229"),
 207       boost::lexical_cast<T>("832040"),
 208       boost::lexical_cast<T>("1346269"),
 209       boost::lexical_cast<T>("2178309"),
 210       boost::lexical_cast<T>("3524578"),
 211       boost::lexical_cast<T>("5702887"),
 212       boost::lexical_cast<T>("9227465"),
 213       boost::lexical_cast<T>("14930352"),
 214       boost::lexical_cast<T>("24157817"),
 215       boost::lexical_cast<T>("39088169"),
 216       boost::lexical_cast<T>("63245986"),
 217       boost::lexical_cast<T>("102334155"),
 218       boost::lexical_cast<T>("165580141"),
 219       boost::lexical_cast<T>("267914296"),
 220       boost::lexical_cast<T>("433494437"),
 221       boost::lexical_cast<T>("701408733"),
 222       boost::lexical_cast<T>("1134903170"),
 223       boost::lexical_cast<T>("1836311903"),
 224       boost::lexical_cast<T>("2971215073"),
 225       // 64-bit:
 226       boost::lexical_cast<T>("4807526976"),
 227       boost::lexical_cast<T>("7778742049"),
 228       boost::lexical_cast<T>("12586269025"),
 229       boost::lexical_cast<T>("20365011074"),
 230       boost::lexical_cast<T>("32951280099"),
 231       boost::lexical_cast<T>("53316291173"),
 232       boost::lexical_cast<T>("86267571272"),
 233       boost::lexical_cast<T>("139583862445"),
 234       boost::lexical_cast<T>("225851433717"),
 235       boost::lexical_cast<T>("365435296162"),
 236       boost::lexical_cast<T>("591286729879"),
 237       boost::lexical_cast<T>("956722026041"),
 238       boost::lexical_cast<T>("1548008755920"),
 239       boost::lexical_cast<T>("2504730781961"),
 240       boost::lexical_cast<T>("4052739537881"),
 241       boost::lexical_cast<T>("6557470319842"),
 242       boost::lexical_cast<T>("10610209857723"),
 243       boost::lexical_cast<T>("17167680177565"),
 244       boost::lexical_cast<T>("27777890035288"),
 245       boost::lexical_cast<T>("44945570212853"),
 246       boost::lexical_cast<T>("72723460248141"),
 247       boost::lexical_cast<T>("117669030460994"),
 248       boost::lexical_cast<T>("190392490709135"),
 249       boost::lexical_cast<T>("308061521170129"),
 250       boost::lexical_cast<T>("498454011879264"),
 251       boost::lexical_cast<T>("806515533049393"),
 252       boost::lexical_cast<T>("1304969544928657"),
 253       boost::lexical_cast<T>("2111485077978050"),
 254       boost::lexical_cast<T>("3416454622906707"),
 255       boost::lexical_cast<T>("5527939700884757"),
 256       boost::lexical_cast<T>("8944394323791464"),
 257       boost::lexical_cast<T>("14472334024676221"),
 258       boost::lexical_cast<T>("23416728348467685"),
 259       boost::lexical_cast<T>("37889062373143906"),
 260       boost::lexical_cast<T>("61305790721611591"),
 261       boost::lexical_cast<T>("99194853094755497"),
 262       boost::lexical_cast<T>("160500643816367088"),
 263       boost::lexical_cast<T>("259695496911122585"),
 264       boost::lexical_cast<T>("420196140727489673"),
 265       boost::lexical_cast<T>("679891637638612258"),
 266       boost::lexical_cast<T>("1100087778366101931"),
 267       boost::lexical_cast<T>("1779979416004714189"),
 268       boost::lexical_cast<T>("2880067194370816120"),
 269       boost::lexical_cast<T>("4660046610375530309"),
 270       boost::lexical_cast<T>("7540113804746346429"),
 271       boost::lexical_cast<T>("12200160415121876738"),
 272       // 128-bit:
 273       boost::lexical_cast<T>("19740274219868223167"),
 274       boost::lexical_cast<T>("31940434634990099905"),
 275       boost::lexical_cast<T>("51680708854858323072"),
 276       boost::lexical_cast<T>("83621143489848422977"),
 277       boost::lexical_cast<T>("135301852344706746049"),
 278       boost::lexical_cast<T>("218922995834555169026"),
 279       boost::lexical_cast<T>("354224848179261915075"),
 280       boost::lexical_cast<T>("573147844013817084101"),
 281       boost::lexical_cast<T>("927372692193078999176"),
 282       boost::lexical_cast<T>("1500520536206896083277"),
 283       boost::lexical_cast<T>("2427893228399975082453"),
 284       boost::lexical_cast<T>("3928413764606871165730"),
 285       boost::lexical_cast<T>("6356306993006846248183"),
 286       boost::lexical_cast<T>("10284720757613717413913"),
 287       boost::lexical_cast<T>("16641027750620563662096"),
 288       boost::lexical_cast<T>("26925748508234281076009"),
 289       boost::lexical_cast<T>("43566776258854844738105"),
 290       boost::lexical_cast<T>("70492524767089125814114"),
 291       boost::lexical_cast<T>("114059301025943970552219"),
 292       boost::lexical_cast<T>("184551825793033096366333"),
 293       boost::lexical_cast<T>("298611126818977066918552"),
 294       boost::lexical_cast<T>("483162952612010163284885"),
 295       boost::lexical_cast<T>("781774079430987230203437"),
 296       boost::lexical_cast<T>("1264937032042997393488322"),
 297       boost::lexical_cast<T>("2046711111473984623691759"),
 298       boost::lexical_cast<T>("3311648143516982017180081"),
 299       boost::lexical_cast<T>("5358359254990966640871840"),
 300       boost::lexical_cast<T>("8670007398507948658051921"),
 301       boost::lexical_cast<T>("14028366653498915298923761"),
 302       boost::lexical_cast<T>("22698374052006863956975682"),
 303       boost::lexical_cast<T>("36726740705505779255899443"),
 304       boost::lexical_cast<T>("59425114757512643212875125"),
 305       boost::lexical_cast<T>("96151855463018422468774568"),
 306       boost::lexical_cast<T>("155576970220531065681649693"),
 307       boost::lexical_cast<T>("251728825683549488150424261"),
 308       boost::lexical_cast<T>("407305795904080553832073954"),
 309       boost::lexical_cast<T>("659034621587630041982498215"),
 310       boost::lexical_cast<T>("1066340417491710595814572169"),
 311       boost::lexical_cast<T>("1725375039079340637797070384"),
 312       boost::lexical_cast<T>("2791715456571051233611642553"),
 313       boost::lexical_cast<T>("4517090495650391871408712937"),
 314       boost::lexical_cast<T>("7308805952221443105020355490"),
 315       boost::lexical_cast<T>("11825896447871834976429068427"),
 316       boost::lexical_cast<T>("19134702400093278081449423917"),
 317       boost::lexical_cast<T>("30960598847965113057878492344"),
 318       boost::lexical_cast<T>("50095301248058391139327916261"),
 319       boost::lexical_cast<T>("81055900096023504197206408605"),
 320       boost::lexical_cast<T>("131151201344081895336534324866"),
 321       boost::lexical_cast<T>("212207101440105399533740733471"),
 322       boost::lexical_cast<T>("343358302784187294870275058337"),
 323       boost::lexical_cast<T>("555565404224292694404015791808"),
 324       boost::lexical_cast<T>("898923707008479989274290850145"),
 325       boost::lexical_cast<T>("1454489111232772683678306641953"),
 326       boost::lexical_cast<T>("2353412818241252672952597492098"),
 327       boost::lexical_cast<T>("3807901929474025356630904134051"),
 328       boost::lexical_cast<T>("6161314747715278029583501626149"),
 329       boost::lexical_cast<T>("9969216677189303386214405760200"),
 330       boost::lexical_cast<T>("16130531424904581415797907386349"),
 331       boost::lexical_cast<T>("26099748102093884802012313146549"),
 332       boost::lexical_cast<T>("42230279526998466217810220532898"),
 333       boost::lexical_cast<T>("68330027629092351019822533679447"),
 334       boost::lexical_cast<T>("110560307156090817237632754212345"),
 335       boost::lexical_cast<T>("178890334785183168257455287891792"),
 336       boost::lexical_cast<T>("289450641941273985495088042104137"),
 337       boost::lexical_cast<T>("468340976726457153752543329995929"),
 338       boost::lexical_cast<T>("757791618667731139247631372100066"),
 339       boost::lexical_cast<T>("1226132595394188293000174702095995"),
 340       boost::lexical_cast<T>("1983924214061919432247806074196061"),
 341       boost::lexical_cast<T>("3210056809456107725247980776292056"),
 342       boost::lexical_cast<T>("5193981023518027157495786850488117"),
 343       boost::lexical_cast<T>("8404037832974134882743767626780173"),
 344       boost::lexical_cast<T>("13598018856492162040239554477268290"),
 345       boost::lexical_cast<T>("22002056689466296922983322104048463"),
 346       boost::lexical_cast<T>("35600075545958458963222876581316753"),
 347       boost::lexical_cast<T>("57602132235424755886206198685365216"),
 348       boost::lexical_cast<T>("93202207781383214849429075266681969"),
 349       boost::lexical_cast<T>("150804340016807970735635273952047185"),
 350       boost::lexical_cast<T>("244006547798191185585064349218729154"),
 351       boost::lexical_cast<T>("394810887814999156320699623170776339"),
 352       boost::lexical_cast<T>("638817435613190341905763972389505493"),
 353       boost::lexical_cast<T>("1033628323428189498226463595560281832"),
 354       boost::lexical_cast<T>("1672445759041379840132227567949787325"),
 355       boost::lexical_cast<T>("2706074082469569338358691163510069157"),
 356       boost::lexical_cast<T>("4378519841510949178490918731459856482"),
 357       boost::lexical_cast<T>("7084593923980518516849609894969925639"),
 358       boost::lexical_cast<T>("11463113765491467695340528626429782121"),
 359       boost::lexical_cast<T>("18547707689471986212190138521399707760"),
 360       boost::lexical_cast<T>("30010821454963453907530667147829489881"),
 361       boost::lexical_cast<T>("48558529144435440119720805669229197641"),
 362       boost::lexical_cast<T>("78569350599398894027251472817058687522"),
 363       boost::lexical_cast<T>("127127879743834334146972278486287885163"),
 364       boost::lexical_cast<T>("205697230343233228174223751303346572685"),
 365       boost::lexical_cast<T>("332825110087067562321196029789634457848"),
 366       boost::lexical_cast<T>("538522340430300790495419781092981030533"),
 367       boost::lexical_cast<T>("871347450517368352816615810882615488381"),
 368       boost::lexical_cast<T>("1409869790947669143312035591975596518914"),
 369       boost::lexical_cast<T>("2281217241465037496128651402858212007295"),
 370       boost::lexical_cast<T>("3691087032412706639440686994833808526209"),
 371       boost::lexical_cast<T>("5972304273877744135569338397692020533504"),
 372       boost::lexical_cast<T>("9663391306290450775010025392525829059713"),
 373       boost::lexical_cast<T>("15635695580168194910579363790217849593217"),
 374       boost::lexical_cast<T>("25299086886458645685589389182743678652930"),
 375       boost::lexical_cast<T>("40934782466626840596168752972961528246147"),
 376       boost::lexical_cast<T>("66233869353085486281758142155705206899077"),
 377       boost::lexical_cast<T>("107168651819712326877926895128666735145224"),
 378       boost::lexical_cast<T>("173402521172797813159685037284371942044301"),
 379       boost::lexical_cast<T>("280571172992510140037611932413038677189525"),
 380       boost::lexical_cast<T>("453973694165307953197296969697410619233826"),
 381       boost::lexical_cast<T>("734544867157818093234908902110449296423351"),
 382       boost::lexical_cast<T>("1188518561323126046432205871807859915657177"),
 383       boost::lexical_cast<T>("1923063428480944139667114773918309212080528"),
 384       boost::lexical_cast<T>("3111581989804070186099320645726169127737705"),
 385       boost::lexical_cast<T>("5034645418285014325766435419644478339818233"),
 386       boost::lexical_cast<T>("8146227408089084511865756065370647467555938"),
 387       boost::lexical_cast<T>("13180872826374098837632191485015125807374171"),
 388       boost::lexical_cast<T>("21327100234463183349497947550385773274930109"),
 389       boost::lexical_cast<T>("34507973060837282187130139035400899082304280"),
 390       boost::lexical_cast<T>("55835073295300465536628086585786672357234389"),
 391       boost::lexical_cast<T>("90343046356137747723758225621187571439538669"),
 392       boost::lexical_cast<T>("146178119651438213260386312206974243796773058"),
 393       boost::lexical_cast<T>("236521166007575960984144537828161815236311727"),
 394       boost::lexical_cast<T>("382699285659014174244530850035136059033084785"),
 395       boost::lexical_cast<T>("619220451666590135228675387863297874269396512"),
 396       boost::lexical_cast<T>("1001919737325604309473206237898433933302481297"),
 397       boost::lexical_cast<T>("1621140188992194444701881625761731807571877809"),
 398       boost::lexical_cast<T>("2623059926317798754175087863660165740874359106"),
 399       boost::lexical_cast<T>("4244200115309993198876969489421897548446236915"),
 400       boost::lexical_cast<T>("6867260041627791953052057353082063289320596021"),
 401       boost::lexical_cast<T>("11111460156937785151929026842503960837766832936"),
 402       boost::lexical_cast<T>("17978720198565577104981084195586024127087428957"),
 403       boost::lexical_cast<T>("29090180355503362256910111038089984964854261893"),
 404       boost::lexical_cast<T>("47068900554068939361891195233676009091941690850"),
 405       boost::lexical_cast<T>("76159080909572301618801306271765994056795952743"),
 406       boost::lexical_cast<T>("123227981463641240980692501505442003148737643593"),
 407       boost::lexical_cast<T>("199387062373213542599493807777207997205533596336"),
 408       boost::lexical_cast<T>("322615043836854783580186309282650000354271239929"),
 409       boost::lexical_cast<T>("522002106210068326179680117059857997559804836265"),
 410       boost::lexical_cast<T>("844617150046923109759866426342507997914076076194"),
 411       boost::lexical_cast<T>("1366619256256991435939546543402365995473880912459"),
 412       boost::lexical_cast<T>("2211236406303914545699412969744873993387956988653"),
 413       boost::lexical_cast<T>("3577855662560905981638959513147239988861837901112"),
 414       boost::lexical_cast<T>("5789092068864820527338372482892113982249794889765"),
 415       boost::lexical_cast<T>("9366947731425726508977331996039353971111632790877"),
 416       boost::lexical_cast<T>("15156039800290547036315704478931467953361427680642"),
 417       boost::lexical_cast<T>("24522987531716273545293036474970821924473060471519"),
 418       boost::lexical_cast<T>("39679027332006820581608740953902289877834488152161"),
 419       boost::lexical_cast<T>("64202014863723094126901777428873111802307548623680"),
 420       boost::lexical_cast<T>("103881042195729914708510518382775401680142036775841"),
 421       boost::lexical_cast<T>("168083057059453008835412295811648513482449585399521"),
 422       boost::lexical_cast<T>("271964099255182923543922814194423915162591622175362"),
 423       boost::lexical_cast<T>("440047156314635932379335110006072428645041207574883"),
 424       boost::lexical_cast<T>("712011255569818855923257924200496343807632829750245"),
 425       boost::lexical_cast<T>("1152058411884454788302593034206568772452674037325128"),
 426       boost::lexical_cast<T>("1864069667454273644225850958407065116260306867075373"),
 427       boost::lexical_cast<T>("3016128079338728432528443992613633888712980904400501"),
 428       boost::lexical_cast<T>("4880197746793002076754294951020699004973287771475874"),
 429       boost::lexical_cast<T>("7896325826131730509282738943634332893686268675876375"),
 430       boost::lexical_cast<T>("12776523572924732586037033894655031898659556447352249"),
 431       boost::lexical_cast<T>("20672849399056463095319772838289364792345825123228624"),
 432       boost::lexical_cast<T>("33449372971981195681356806732944396691005381570580873"),
 433       boost::lexical_cast<T>("54122222371037658776676579571233761483351206693809497"),
 434       boost::lexical_cast<T>("87571595343018854458033386304178158174356588264390370"),
 435       boost::lexical_cast<T>("141693817714056513234709965875411919657707794958199867"),
 436       boost::lexical_cast<T>("229265413057075367692743352179590077832064383222590237"),
 437       boost::lexical_cast<T>("370959230771131880927453318055001997489772178180790104"),
 438       boost::lexical_cast<T>("600224643828207248620196670234592075321836561403380341"),
 439       boost::lexical_cast<T>("971183874599339129547649988289594072811608739584170445"),
 440       boost::lexical_cast<T>("1571408518427546378167846658524186148133445300987550786"),
 441       boost::lexical_cast<T>("2542592393026885507715496646813780220945054040571721231"),
 442       boost::lexical_cast<T>("4114000911454431885883343305337966369078499341559272017"),
 443       boost::lexical_cast<T>("6656593304481317393598839952151746590023553382130993248"),
 444       boost::lexical_cast<T>("10770594215935749279482183257489712959102052723690265265"),
 445       boost::lexical_cast<T>("17427187520417066673081023209641459549125606105821258513"),
 446       boost::lexical_cast<T>("28197781736352815952563206467131172508227658829511523778"),
 447       boost::lexical_cast<T>("45624969256769882625644229676772632057353264935332782291"),
 448       boost::lexical_cast<T>("73822750993122698578207436143903804565580923764844306069"),
 449       boost::lexical_cast<T>("119447720249892581203851665820676436622934188700177088360"),
 450       boost::lexical_cast<T>("193270471243015279782059101964580241188515112465021394429"),
 451       boost::lexical_cast<T>("312718191492907860985910767785256677811449301165198482789"),
 452       boost::lexical_cast<T>("505988662735923140767969869749836918999964413630219877218"),
 453       boost::lexical_cast<T>("818706854228831001753880637535093596811413714795418360007"),
 454       boost::lexical_cast<T>("1324695516964754142521850507284930515811378128425638237225"),
 455       boost::lexical_cast<T>("2143402371193585144275731144820024112622791843221056597232"),
 456       boost::lexical_cast<T>("3468097888158339286797581652104954628434169971646694834457"),
 457       boost::lexical_cast<T>("5611500259351924431073312796924978741056961814867751431689"),
 458       boost::lexical_cast<T>("9079598147510263717870894449029933369491131786514446266146"),
 459       boost::lexical_cast<T>("14691098406862188148944207245954912110548093601382197697835"),
 460       boost::lexical_cast<T>("23770696554372451866815101694984845480039225387896643963981"),
 461       boost::lexical_cast<T>("38461794961234640015759308940939757590587318989278841661816"),
 462       boost::lexical_cast<T>("62232491515607091882574410635924603070626544377175485625797"),
 463       boost::lexical_cast<T>("100694286476841731898333719576864360661213863366454327287613"),
 464       boost::lexical_cast<T>("162926777992448823780908130212788963731840407743629812913410"),
 465       boost::lexical_cast<T>("263621064469290555679241849789653324393054271110084140201023"),
 466       boost::lexical_cast<T>("426547842461739379460149980002442288124894678853713953114433"),
 467       boost::lexical_cast<T>("690168906931029935139391829792095612517948949963798093315456"),
 468       boost::lexical_cast<T>("1116716749392769314599541809794537900642843628817512046429889"),
 469       boost::lexical_cast<T>("1806885656323799249738933639586633513160792578781310139745345"),
 470       boost::lexical_cast<T>("2923602405716568564338475449381171413803636207598822186175234"),
 471       boost::lexical_cast<T>("4730488062040367814077409088967804926964428786380132325920579"),
 472       boost::lexical_cast<T>("7654090467756936378415884538348976340768064993978954512095813"),
 473       boost::lexical_cast<T>("12384578529797304192493293627316781267732493780359086838016392"),
 474       boost::lexical_cast<T>("20038668997554240570909178165665757608500558774338041350112205"),
 475       boost::lexical_cast<T>("32423247527351544763402471792982538876233052554697128188128597"),
 476       boost::lexical_cast<T>("52461916524905785334311649958648296484733611329035169538240802"),
 477       boost::lexical_cast<T>("84885164052257330097714121751630835360966663883732297726369399"),
 478       boost::lexical_cast<T>("137347080577163115432025771710279131845700275212767467264610201"),
 479       boost::lexical_cast<T>("222232244629420445529739893461909967206666939096499764990979600"),
 480       boost::lexical_cast<T>("359579325206583560961765665172189099052367214309267232255589801"),
 481       boost::lexical_cast<T>("581811569836004006491505558634099066259034153405766997246569401"),
 482       boost::lexical_cast<T>("941390895042587567453271223806288165311401367715034229502159202"),
 483       boost::lexical_cast<T>("1523202464878591573944776782440387231570435521120801226748728603"),
 484       boost::lexical_cast<T>("2464593359921179141398048006246675396881836888835835456250887805"),
 485       boost::lexical_cast<T>("3987795824799770715342824788687062628452272409956636682999616408"),
 486       boost::lexical_cast<T>("6452389184720949856740872794933738025334109298792472139250504213"),
 487       boost::lexical_cast<T>("10440185009520720572083697583620800653786381708749108822250120621"),
 488       boost::lexical_cast<T>("16892574194241670428824570378554538679120491007541580961500624834"),
 489       boost::lexical_cast<T>("27332759203762391000908267962175339332906872716290689783750745455"),
 490       boost::lexical_cast<T>("44225333398004061429732838340729878012027363723832270745251370289"),
 491       boost::lexical_cast<T>("71558092601766452430641106302905217344934236440122960529002115744"),
 492       boost::lexical_cast<T>("115783425999770513860373944643635095356961600163955231274253486033"),
 493       boost::lexical_cast<T>("187341518601536966291015050946540312701895836604078191803255601777"),
 494       boost::lexical_cast<T>("303124944601307480151388995590175408058857436768033423077509087810"),
 495       boost::lexical_cast<T>("490466463202844446442404046536715720760753273372111614880764689587"),
 496       boost::lexical_cast<T>("793591407804151926593793042126891128819610710140145037958273777397"),
 497       boost::lexical_cast<T>("1284057871006996373036197088663606849580363983512256652839038466984"),
 498       boost::lexical_cast<T>("2077649278811148299629990130790497978399974693652401690797312244381"),
 499       boost::lexical_cast<T>("3361707149818144672666187219454104827980338677164658343636350711365"),
 500       boost::lexical_cast<T>("5439356428629292972296177350244602806380313370817060034433662955746"),
 501       boost::lexical_cast<T>("8801063578447437644962364569698707634360652047981718378070013667111"),
 502       boost::lexical_cast<T>("14240420007076730617258541919943310440740965418798778412503676622857"),
 503       boost::lexical_cast<T>("23041483585524168262220906489642018075101617466780496790573690289968"),
 504       boost::lexical_cast<T>("37281903592600898879479448409585328515842582885579275203077366912825"),
 505       boost::lexical_cast<T>("60323387178125067141700354899227346590944200352359771993651057202793"),
 506       boost::lexical_cast<T>("97605290770725966021179803308812675106786783237939047196728424115618"),
 507       boost::lexical_cast<T>("157928677948851033162880158208040021697730983590298819190379481318411"),
 508       boost::lexical_cast<T>("255533968719576999184059961516852696804517766828237866387107905434029"),
 509       boost::lexical_cast<T>("413462646668428032346940119724892718502248750418536685577487386752440"),
 510       boost::lexical_cast<T>("668996615388005031531000081241745415306766517246774551964595292186469"),
 511       boost::lexical_cast<T>("1082459262056433063877940200966638133809015267665311237542082678938909"),
 512       boost::lexical_cast<T>("1751455877444438095408940282208383549115781784912085789506677971125378"),
 513       boost::lexical_cast<T>("2833915139500871159286880483175021682924797052577397027048760650064287"),
 514       boost::lexical_cast<T>("4585371016945309254695820765383405232040578837489482816555438621189665"),
 515       boost::lexical_cast<T>("7419286156446180413982701248558426914965375890066879843604199271253952"),
 516       boost::lexical_cast<T>("12004657173391489668678522013941832147005954727556362660159637892443617"),
 517       boost::lexical_cast<T>("19423943329837670082661223262500259061971330617623242503763837163697569"),
 518       boost::lexical_cast<T>("31428600503229159751339745276442091208977285345179605163923475056141186"),
 519       boost::lexical_cast<T>("50852543833066829834000968538942350270948615962802847667687312219838755"),
 520       boost::lexical_cast<T>("82281144336295989585340713815384441479925901307982452831610787275979941"),
 521       boost::lexical_cast<T>("133133688169362819419341682354326791750874517270785300499298099495818696"),
 522       boost::lexical_cast<T>("215414832505658809004682396169711233230800418578767753330908886771798637"),
 523       boost::lexical_cast<T>("348548520675021628424024078524038024981674935849553053830206986267617333"),
 524       boost::lexical_cast<T>("563963353180680437428706474693749258212475354428320807161115873039415970"),
 525       boost::lexical_cast<T>("912511873855702065852730553217787283194150290277873860991322859307033303"),
 526       boost::lexical_cast<T>("1476475227036382503281437027911536541406625644706194668152438732346449273"),
 527       boost::lexical_cast<T>("2388987100892084569134167581129323824600775934984068529143761591653482576"),
 528       boost::lexical_cast<T>("3865462327928467072415604609040860366007401579690263197296200323999931849"),
 529       boost::lexical_cast<T>("6254449428820551641549772190170184190608177514674331726439961915653414425"),
 530       boost::lexical_cast<T>("10119911756749018713965376799211044556615579094364594923736162239653346274"),
 531       boost::lexical_cast<T>("16374361185569570355515148989381228747223756609038926650176124155306760699"),
 532       boost::lexical_cast<T>("26494272942318589069480525788592273303839335703403521573912286394960106973"),
 533       boost::lexical_cast<T>("42868634127888159424995674777973502051063092312442448224088410550266867672"),
 534       boost::lexical_cast<T>("69362907070206748494476200566565775354902428015845969798000696945226974645"),
 535       boost::lexical_cast<T>("112231541198094907919471875344539277405965520328288418022089107495493842317"),
 536       boost::lexical_cast<T>("181594448268301656413948075911105052760867948344134387820089804440720816962"),
 537       boost::lexical_cast<T>("293825989466396564333419951255644330166833468672422805842178911936214659279"),
 538       boost::lexical_cast<T>("475420437734698220747368027166749382927701417016557193662268716376935476241"),
 539       boost::lexical_cast<T>("769246427201094785080787978422393713094534885688979999504447628313150135520"),
 540       boost::lexical_cast<T>("1244666864935793005828156005589143096022236302705537193166716344690085611761"),
 541       boost::lexical_cast<T>("2013913292136887790908943984011536809116771188394517192671163973003235747281"),
 542       boost::lexical_cast<T>("3258580157072680796737099989600679905139007491100054385837880317693321359042"),
 543       boost::lexical_cast<T>("5272493449209568587646043973612216714255778679494571578509044290696557106323"),
 544       boost::lexical_cast<T>("8531073606282249384383143963212896619394786170594625964346924608389878465365"),
 545       boost::lexical_cast<T>("13803567055491817972029187936825113333650564850089197542855968899086435571688"),
 546       boost::lexical_cast<T>("22334640661774067356412331900038009953045351020683823507202893507476314037053"),
 547       boost::lexical_cast<T>("36138207717265885328441519836863123286695915870773021050058862406562749608741"),
 548       boost::lexical_cast<T>("58472848379039952684853851736901133239741266891456844557261755914039063645794"),
 549       boost::lexical_cast<T>("94611056096305838013295371573764256526437182762229865607320618320601813254535"),
 550       boost::lexical_cast<T>("153083904475345790698149223310665389766178449653686710164582374234640876900329"),
 551       boost::lexical_cast<T>("247694960571651628711444594884429646292615632415916575771902992555242690154864"),
 552       boost::lexical_cast<T>("400778865046997419409593818195095036058794082069603285936485366789883567055193"),
 553       boost::lexical_cast<T>("648473825618649048121038413079524682351409714485519861708388359345126257210057"),
 554       boost::lexical_cast<T>("1049252690665646467530632231274619718410203796555123147644873726135009824265250"),
 555       boost::lexical_cast<T>("1697726516284295515651670644354144400761613511040643009353262085480136081475307"),
 556       boost::lexical_cast<T>("2746979206949941983182302875628764119171817307595766156998135811615145905740557"),
 557       boost::lexical_cast<T>("4444705723234237498833973519982908519933430818636409166351397897095281987215864"),
 558       boost::lexical_cast<T>("7191684930184179482016276395611672639105248126232175323349533708710427892956421"),
 559       boost::lexical_cast<T>("11636390653418416980850249915594581159038678944868584489700931605805709880172285"),
 560       boost::lexical_cast<T>("18828075583602596462866526311206253798143927071100759813050465314516137773128706"),
 561       boost::lexical_cast<T>("30464466237021013443716776226800834957182606015969344302751396920321847653300991"),
 562       boost::lexical_cast<T>("49292541820623609906583302538007088755326533087070104115801862234837985426429697"),
 563       boost::lexical_cast<T>("79757008057644623350300078764807923712509139103039448418553259155159833079730688"),
 564       boost::lexical_cast<T>("129049549878268233256883381302815012467835672190109552534355121389997818506160385"),
 565       boost::lexical_cast<T>("208806557935912856607183460067622936180344811293149000952908380545157651585891073"),
 566       boost::lexical_cast<T>("337856107814181089864066841370437948648180483483258553487263501935155470092051458"),
 567       boost::lexical_cast<T>("546662665750093946471250301438060884828525294776407554440171882480313121677942531"),
 568       boost::lexical_cast<T>("884518773564275036335317142808498833476705778259666107927435384415468591769993989"),
 569       boost::lexical_cast<T>("1431181439314368982806567444246559718305231073036073662367607266895781713447936520"),
 570       boost::lexical_cast<T>("2315700212878644019141884587055058551781936851295739770295042651311250305217930509"),
 571       boost::lexical_cast<T>("3746881652193013001948452031301618270087167924331813432662649918207032018665867029"),
 572       boost::lexical_cast<T>("6062581865071657021090336618356676821869104775627553202957692569518282323883797538"),
 573       boost::lexical_cast<T>("9809463517264670023038788649658295091956272699959366635620342487725314342549664567"),
 574       boost::lexical_cast<T>("15872045382336327044129125268014971913825377475586919838578035057243596666433462105"),
 575       boost::lexical_cast<T>("25681508899600997067167913917673267005781650175546286474198377544968911008983126672"),
 576       boost::lexical_cast<T>("41553554281937324111297039185688238919607027651133206312776412602212507675416588777"),
 577       boost::lexical_cast<T>("67235063181538321178464953103361505925388677826679492786974790147181418684399715449"),
 578       boost::lexical_cast<T>("108788617463475645289761992289049744844995705477812699099751202749393926359816304226"),
 579       boost::lexical_cast<T>("176023680645013966468226945392411250770384383304492191886725992896575345044216019675"),
 580       boost::lexical_cast<T>("284812298108489611757988937681460995615380088782304890986477195645969271404032323901"),
 581       boost::lexical_cast<T>("460835978753503578226215883073872246385764472086797082873203188542544616448248343576"),
 582       boost::lexical_cast<T>("745648276861993189984204820755333242001144560869101973859680384188513887852280667477"),
 583       boost::lexical_cast<T>("1206484255615496768210420703829205488386909032955899056732883572731058504300529011053"),
 584       boost::lexical_cast<T>("1952132532477489958194625524584538730388053593825001030592563956919572392152809678530"),
 585       boost::lexical_cast<T>("3158616788092986726405046228413744218774962626780900087325447529650630896453338689583"),
 586       boost::lexical_cast<T>("5110749320570476684599671752998282949163016220605901117918011486570203288606148368113"),
 587       boost::lexical_cast<T>("8269366108663463411004717981412027167937978847386801205243459016220834185059487057696"),
 588       boost::lexical_cast<T>("13380115429233940095604389734410310117100995067992702323161470502791037473665635425809"),
 589       boost::lexical_cast<T>("21649481537897403506609107715822337285038973915379503528404929519011871658725122483505"),
 590       boost::lexical_cast<T>("35029596967131343602213497450232647402139968983372205851566400021802909132390757909314"),
 591       boost::lexical_cast<T>("56679078505028747108822605166054984687178942898751709379971329540814780791115880392819"),
 592       boost::lexical_cast<T>("91708675472160090711036102616287632089318911882123915231537729562617689923506638302133"),
 593       boost::lexical_cast<T>("148387753977188837819858707782342616776497854780875624611509059103432470714622518694952"),
 594       boost::lexical_cast<T>("240096429449348928530894810398630248865816766662999539843046788666050160638129156997085"),
 595       boost::lexical_cast<T>("388484183426537766350753518180972865642314621443875164454555847769482631352751675692037"),
 596       boost::lexical_cast<T>("628580612875886694881648328579603114508131388106874704297602636435532791990880832689122"),
 597       boost::lexical_cast<T>("1017064796302424461232401846760575980150446009550749868752158484205015423343632508381159"),
 598       boost::lexical_cast<T>("1645645409178311156114050175340179094658577397657624573049761120640548215334513341070281"),
 599       boost::lexical_cast<T>("2662710205480735617346452022100755074809023407208374441801919604845563638678145849451440"),
 600       boost::lexical_cast<T>("4308355614659046773460502197440934169467600804865999014851680725486111854012659190521721"),
 601       boost::lexical_cast<T>("6971065820139782390806954219541689244276624212074373456653600330331675492690805039973161"),
 602       boost::lexical_cast<T>("11279421434798829164267456416982623413744225016940372471505281055817787346703464230494882"),
 603       boost::lexical_cast<T>("18250487254938611555074410636524312658020849229014745928158881386149462839394269270468043"),
 604       boost::lexical_cast<T>("29529908689737440719341867053506936071765074245955118399664162441967250186097733500962925"),
 605       boost::lexical_cast<T>("47780395944676052274416277690031248729785923474969864327823043828116713025492002771430968"),
 606       boost::lexical_cast<T>("77310304634413492993758144743538184801550997720924982727487206270083963211589736272393893"),
 607       boost::lexical_cast<T>("125090700579089545268174422433569433531336921195894847055310250098200676237081739043824861"),
 608       boost::lexical_cast<T>("202401005213503038261932567177107618332887918916819829782797456368284639448671475316218754"),
 609       boost::lexical_cast<T>("327491705792592583530106989610677051864224840112714676838107706466485315685753214360043615"),
 610       boost::lexical_cast<T>("529892711006095621792039556787784670197112759029534506620905162834769955134424689676262369"),
 611       boost::lexical_cast<T>("857384416798688205322146546398461722061337599142249183459012869301255270820177904036305984"),
 612       boost::lexical_cast<T>("1387277127804783827114186103186246392258450358171783690079918032136025225954602593712568353"),
 613       boost::lexical_cast<T>("2244661544603472032436332649584708114319787957314032873538930901437280496774780497748874337"),
 614       boost::lexical_cast<T>("3631938672408255859550518752770954506578238315485816563618848933573305722729383091461442690"),
 615       boost::lexical_cast<T>("5876600217011727891986851402355662620898026272799849437157779835010586219504163589210317027"),
 616       boost::lexical_cast<T>("9508538889419983751537370155126617127476264588285666000776628768583891942233546680671759717"),
 617       boost::lexical_cast<T>("15385139106431711643524221557482279748374290861085515437934408603594478161737710269882076744"),
 618       boost::lexical_cast<T>("24893677995851695395061591712608896875850555449371181438711037372178370103971256950553836461"),
 619       boost::lexical_cast<T>("40278817102283407038585813270091176624224846310456696876645445975772848265708967220435913205"),
 620       boost::lexical_cast<T>("65172495098135102433647404982700073500075401759827878315356483347951218369680224170989749666"),
 621       boost::lexical_cast<T>("105451312200418509472233218252791250124300248070284575192001929323724066635389191391425662871"),
 622       boost::lexical_cast<T>("170623807298553611905880623235491323624375649830112453507358412671675285005069415562415412537"),
 623       boost::lexical_cast<T>("276075119498972121378113841488282573748675897900397028699360341995399351640458606953841075408"),
 624       boost::lexical_cast<T>("446698926797525733283994464723773897373051547730509482206718754667074636645528022516256487945"),
 625       boost::lexical_cast<T>("722774046296497854662108306212056471121727445630906510906079096662473988285986629470097563353"),
 626       boost::lexical_cast<T>("1169472973094023587946102770935830368494778993361415993112797851329548624931514651986354051298"),
 627       boost::lexical_cast<T>("1892247019390521442608211077147886839616506438992322504018876947992022613217501281456451614651"),
 628       boost::lexical_cast<T>("3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949"),
 629       boost::lexical_cast<T>("4953967011875066473162524925231604047727791871346061001150551747313593851366517214899257280600"),
 630       boost::lexical_cast<T>("8015687004359611503716838773315321255839077303699799498282226546635165089515533148342062946549"),
 631       boost::lexical_cast<T>("12969654016234677976879363698546925303566869175045860499432778293948758940882050363241320227149"),
 632       boost::lexical_cast<T>("20985341020594289480596202471862246559405946478745659997715004840583924030397583511583383173698"),
 633       boost::lexical_cast<T>("33954995036828967457475566170409171862972815653791520497147783134532682971279633874824703400847"),
 634       boost::lexical_cast<T>("54940336057423256938071768642271418422378762132537180494862787975116607001677217386408086574545"),
 635       boost::lexical_cast<T>("88895331094252224395547334812680590285351577786328700992010571109649289972956851261232789975392"),
 636       boost::lexical_cast<T>("143835667151675481333619103454952008707730339918865881486873359084765896974634068647640876549937"),
 637       boost::lexical_cast<T>("232730998245927705729166438267632598993081917705194582478883930194415186947590919908873666525329"),
 638       boost::lexical_cast<T>("376566665397603187062785541722584607700812257624060463965757289279181083922224988556514543075266"),
 639       boost::lexical_cast<T>("609297663643530892791951979990217206693894175329255046444641219473596270869815908465388209600595"),
 640       boost::lexical_cast<T>("985864329041134079854737521712801814394706432953315510410398508752777354792040897021902752675861"),
 641       boost::lexical_cast<T>("1595161992684664972646689501703019021088600608282570556855039728226373625661856805487290962276456"),
 642       boost::lexical_cast<T>("2581026321725799052501427023415820835483307041235886067265438236979150980453897702509193714952317"),
 643       boost::lexical_cast<T>("4176188314410464025148116525118839856571907649518456624120477965205524606115754507996484677228773"),
 644       boost::lexical_cast<T>("6757214636136263077649543548534660692055214690754342691385916202184675586569652210505678392181090"),
 645       boost::lexical_cast<T>("10933402950546727102797660073653500548627122340272799315506394167390200192685406718502163069409863"),
 646       boost::lexical_cast<T>("17690617586682990180447203622188161240682337031027142006892310369574875779255058929007841461590953"),
 647       boost::lexical_cast<T>("28624020537229717283244863695841661789309459371299941322398704536965075971940465647510004531000816"),
 648       boost::lexical_cast<T>("46314638123912707463692067318029823029991796402327083329291014906539951751195524576517845992591769"),
 649       boost::lexical_cast<T>("74938658661142424746936931013871484819301255773627024651689719443505027723135990224027850523592585"),
 650       boost::lexical_cast<T>("121253296785055132210628998331901307849293052175954107980980734350044979474331514800545696516184354"),
 651       boost::lexical_cast<T>("196191955446197556957565929345772792668594307949581132632670453793550007197467505024573547039776939"),
 652       boost::lexical_cast<T>("317445252231252689168194927677674100517887360125535240613651188143594986671799019825119243555961293"),
 653       boost::lexical_cast<T>("513637207677450246125760857023446893186481668075116373246321641937144993869266524849692790595738232"),
 654       boost::lexical_cast<T>("831082459908702935293955784701120993704369028200651613859972830080739980541065544674812034151699525"),
 655       boost::lexical_cast<T>("1344719667586153181419716641724567886890850696275767987106294472017884974410332069524504824747437757"),
 656       boost::lexical_cast<T>("2175802127494856116713672426425688880595219724476419600966267302098624954951397614199316858899137282"),
 657       boost::lexical_cast<T>("3520521795081009298133389068150256767486070420752187588072561774116509929361729683723821683646575039"),
 658       boost::lexical_cast<T>("5696323922575865414847061494575945648081290145228607189038829076215134884313127297923138542545712321"),
 659       boost::lexical_cast<T>("9216845717656874712980450562726202415567360565980794777111390850331644813674856981646960226192287360"),
 660       boost::lexical_cast<T>("14913169640232740127827512057302148063648650711209401966150219926546779697987984279570098768737999681"),
 661       boost::lexical_cast<T>("24130015357889614840807962620028350479216011277190196743261610776878424511662841261217058994930287041"),
 662       boost::lexical_cast<T>("39043184998122354968635474677330498542864661988399598709411830703425204209650825540787157763668286722"),
 663       boost::lexical_cast<T>("63173200356011969809443437297358849022080673265589795452673441480303628721313666802004216758598573763"),
 664       boost::lexical_cast<T>("102216385354134324778078911974689347564945335253989394162085272183728832930964492342791374522266860485"),
 665       boost::lexical_cast<T>("165389585710146294587522349272048196587026008519579189614758713664032461652278159144795591280865434248"),
 666       boost::lexical_cast<T>("267605971064280619365601261246737544151971343773568583776843985847761294583242651487586965803132294733"),
 667       boost::lexical_cast<T>("432995556774426913953123610518785740738997352293147773391602699511793756235520810632382557083997728981"),
 668       boost::lexical_cast<T>("700601527838707533318724871765523284890968696066716357168446685359555050818763462119969522887130023714"),
 669       boost::lexical_cast<T>("1133597084613134447271848482284309025629966048359864130560049384871348807054284272752352079971127752695"),
 670       boost::lexical_cast<T>("1834198612451841980590573354049832310520934744426580487728496070230903857873047734872321602858257776409"),
 671       boost::lexical_cast<T>("2967795697064976427862421836334141336150900792786444618288545455102252664927332007624673682829385529104"),
 672       boost::lexical_cast<T>("4801994309516818408452995190383973646671835537213025106017041525333156522800379742496995285687643305513"),
 673       boost::lexical_cast<T>("7769790006581794836315417026718114982822736329999469724305586980435409187727711750121668968517028834617"),
 674       boost::lexical_cast<T>("12571784316098613244768412217102088629494571867212494830322628505768565710528091492618664254204672140130"),
 675       boost::lexical_cast<T>("20341574322680408081083829243820203612317308197211964554628215486203974898255803242740333222721700974747"),
 676       boost::lexical_cast<T>("32913358638779021325852241460922292241811880064424459384950843991972540608783894735358997476926373114877"),
 677       boost::lexical_cast<T>("53254932961459429406936070704742495854129188261636423939579059478176515507039697978099330699648074089624"),
 678       boost::lexical_cast<T>("86168291600238450732788312165664788095941068326060883324529903470149056115823592713458328176574447204501"),
 679       boost::lexical_cast<T>("139423224561697880139724382870407283950070256587697307264108962948325571622863290691557658876222521294125"),
 680       boost::lexical_cast<T>("225591516161936330872512695036072072046011324913758190588638866418474627738686883405015987052796968498626"),
 681       boost::lexical_cast<T>("365014740723634211012237077906479355996081581501455497852747829366800199361550174096573645929019489792751"),
 682       boost::lexical_cast<T>("590606256885570541884749772942551428042092906415213688441386695785274827100237057501589632981816458291377"),
 683       boost::lexical_cast<T>("955620997609204752896986850849030784038174487916669186294134525152075026461787231598163278910835948084128"),
 684       boost::lexical_cast<T>("1546227254494775294781736623791582212080267394331882874735521220937349853562024289099752911892652406375505"),
 685       boost::lexical_cast<T>("2501848252103980047678723474640612996118441882248552061029655746089424880023811520697916190803488354459633"),
 686       boost::lexical_cast<T>("4048075506598755342460460098432195208198709276580434935765176967026774733585835809797669102696140760835138"),
 687       boost::lexical_cast<T>("6549923758702735390139183573072808204317151158828986996794832713116199613609647330495585293499629115294771"),
 688       boost::lexical_cast<T>("10597999265301490732599643671505003412515860435409421932560009680142974347195483140293254396195769876129909"),
 689       boost::lexical_cast<T>("17147923024004226122738827244577811616833011594238408929354842393259173960805130470788839689695398991424680"),
 690       boost::lexical_cast<T>("27745922289305716855338470916082815029348872029647830861914852073402148308000613611082094085891168867554589"),
 691       boost::lexical_cast<T>("44893845313309942978077298160660626646181883623886239791269694466661322268805744081870933775586567858979269"),
 692       boost::lexical_cast<T>("72639767602615659833415769076743441675530755653534070653184546540063470576806357692953027861477736726533858"),
 693       boost::lexical_cast<T>("117533612915925602811493067237404068321712639277420310444454241006724792845612101774823961637064304585513127"),
 694       boost::lexical_cast<T>("190173380518541262644908836314147509997243394930954381097638787546788263422418459467776989498542041312046985"),
 695       boost::lexical_cast<T>("307706993434466865456401903551551578318956034208374691542093028553513056268030561242600951135606345897560112"),
 696       boost::lexical_cast<T>("497880373953008128101310739865699088316199429139329072639731816100301319690449020710377940634148387209607097"),
 697       boost::lexical_cast<T>("805587367387474993557712643417250666635155463347703764181824844653814375958479581952978891769754733107167209"),
 698       boost::lexical_cast<T>("1303467741340483121659023383282949754951354892487032836821556660754115695648928602663356832403903120316774306"),
 699       boost::lexical_cast<T>("2109055108727958115216736026700200421586510355834736601003381505407930071607408184616335724173657853423941515"),
 700       boost::lexical_cast<T>("3412522850068441236875759409983150176537865248321769437824938166162045767256336787279692556577560973740715821"),
 701       boost::lexical_cast<T>("5521577958796399352092495436683350598124375604156506038828319671569975838863744971896028280751218827164657336"),
 702       boost::lexical_cast<T>("8934100808864840588968254846666500774662240852478275476653257837732021606120081759175720837328779800905373157"),
 703       boost::lexical_cast<T>("14455678767661239941060750283349851372786616456634781515481577509301997444983826731071749118079998628070030493"),
 704       boost::lexical_cast<T>("23389779576526080530029005130016352147448857309113056992134835347034019051103908490247469955408778428975403650"),
 705       boost::lexical_cast<T>("37845458344187320471089755413366203520235473765747838507616412856336016496087735221319219073488777057045434143"),
 706       boost::lexical_cast<T>("61235237920713401001118760543382555667684331074860895499751248203370035547191643711566689028897555486020837793"),
 707       boost::lexical_cast<T>("99080696264900721472208515956748759187919804840608734007367661059706052043279378932885908102386332543066271936"),
 708       boost::lexical_cast<T>("160315934185614122473327276500131314855604135915469629507118909263076087590471022644452597131283888029087109729"),
 709       boost::lexical_cast<T>("259396630450514843945535792456880074043523940756078363514486570322782139633750401577338505233670220572153381665"),
 710       boost::lexical_cast<T>("419712564636128966418863068957011388899128076671547993021605479585858227224221424221791102364954108601240491394"),
 711       boost::lexical_cast<T>("679109195086643810364398861413891462942652017427626356536092049908640366857971825799129607598624329173393873059"),
 712       boost::lexical_cast<T>("1098821759722772776783261930370902851841780094099174349557697529494498594082193250020920709963578437774634364453"),
 713       boost::lexical_cast<T>("1777930954809416587147660791784794314784432111526800706093789579403138960940165075820050317562202766948028237512"),
 714       boost::lexical_cast<T>("2876752714532189363930922722155697166626212205625975055651487108897637555022358325840971027525781204722662601965"),
 715       boost::lexical_cast<T>("4654683669341605951078583513940491481410644317152775761745276688300776515962523401661021345087983971670690839477"),
 716       boost::lexical_cast<T>("7531436383873795315009506236096188648036856522778750817396763797198414070984881727501992372613765176393353441442"),
 717       boost::lexical_cast<T>("12186120053215401266088089750036680129447500839931526579142040485499190586947405129163013717701749148064044280919"),
 718       boost::lexical_cast<T>("19717556437089196581097595986132868777484357362710277396538804282697604657932286856665006090315514324457397722361"),
 719       boost::lexical_cast<T>("31903676490304597847185685736169548906931858202641803975680844768196795244879691985828019808017263472521442003280"),
 720       boost::lexical_cast<T>("51621232927393794428283281722302417684416215565352081372219649050894399902811978842493025898332777796978839725641"),
 721       boost::lexical_cast<T>("83524909417698392275468967458471966591348073767993885347900493819091195147691670828321045706350041269500281728921"),
 722       boost::lexical_cast<T>("135146142345092186703752249180774384275764289333345966720120142869985595050503649670814071604682819066479121454562"),
 723       boost::lexical_cast<T>("218671051762790578979221216639246350867112363101339852068020636689076790198195320499135117311032860335979403183483"),
 724       boost::lexical_cast<T>("353817194107882765682973465820020735142876652434685818788140779559062385248698970169949188915715679402458524638045"),
 725       boost::lexical_cast<T>("572488245870673344662194682459267086009989015536025670856161416248139175446894290669084306226748539738437927821528"),
 726       boost::lexical_cast<T>("926305439978556110345168148279287821152865667970711489644302195807201560695593260839033495142464219140896452459573"),
 727       boost::lexical_cast<T>("1498793685849229455007362830738554907162854683506737160500463612055340736142487551508117801369212758879334380281101"),
 728       boost::lexical_cast<T>("2425099125827785565352530979017842728315720351477448650144765807862542296838080812347151296511676978020230832740674"),
 729       boost::lexical_cast<T>("3923892811677015020359893809756397635478575034984185810645229419917883032980568363855269097880889736899565213021775"),
 730       boost::lexical_cast<T>("6348991937504800585712424788774240363794295386461634460789995227780425329818649176202420394392566714919796045762449"),
 731       boost::lexical_cast<T>("10272884749181815606072318598530637999272870421445820271435224647698308362799217540057689492273456451819361258784224"),
 732       boost::lexical_cast<T>("16621876686686616191784743387304878363067165807907454732225219875478733692617866716260109886666023166739157304546673"),
 733       boost::lexical_cast<T>("26894761435868431797857061985835516362340036229353275003660444523177042055417084256317799378939479618558518563330897"),
 734       boost::lexical_cast<T>("4351663812255504798964180537314039472540720203726072973588566439865577574803495097257790926560550278529767567877570"),
 735       boost::lexical_cast<T>("70411399558423479787498867358975911087747238266614004739546108921832817803452035228895708644544982403856194431208467"),
 736       boost::lexical_cast<T>("113928037680978527777140672732116305813154440303874734475431773320488593551486986201473617910150485189153870299086037"),
 737       boost::lexical_cast<T>("184339437239402007564639540091092216900901678570488739214977882242321411354939021430369326554695467593010064730294504"),
 738       boost::lexical_cast<T>("298267474920380535341780212823208522714056118874363473690409655562810004906426007631842944464845952782163935029380541"),
 739       boost::lexical_cast<T>("482606912159782542906419752914300739614957797444852212905387537805131416261365029062212271019541420375173999759675045"),
 740       boost::lexical_cast<T>("780874387080163078248199965737509262329013916319215686595797193367941421167791036694055215484387373157337934789055586"),
 741       boost::lexical_cast<T>("1263481299239945621154619718651810001943971713764067899501184731173072837429156065756267486503928793532511934548730631"),
 742       boost::lexical_cast<T>("2044355686320108699402819684389319264272985630083283586096981924541014258596947102450322701988316166689849869337786217"),
 743       boost::lexical_cast<T>("3307836985560054320557439403041129266216957343847351485598166655714087096026103168206590188492244960222361803886516848"),
 744       boost::lexical_cast<T>("5352192671880163019960259087430448530489942973930635071695148580255101354623050270656912890480561126912211673224303065"),
 745       boost::lexical_cast<T>("8660029657440217340517698490471577796706900317777986557293315235969188450649153438863503078972806087134573477110819913"),
 746       boost::lexical_cast<T>("14012222329320380360477957577902026327196843291708621628988463816224289805272203709520415969453367214046785150335122978"),
 747       boost::lexical_cast<T>("22672251986760597700995656068373604123903743609486608186281779052193478255921357148383919048426173301181358627445942891"),
 748       boost::lexical_cast<T>("36684474316080978061473613646275630451100586901195229815270242868417768061193560857904335017879540515228143777781065869"),
 749       boost::lexical_cast<T>("59356726302841575762469269714649234575004330510681838001552021920611246317114918006288254066305713816409502405227008760"),
 750       boost::lexical_cast<T>("96041200618922553823942883360924865026104917411877067816822264789029014378308478864192589084185254331637646183008074629"),
 751       boost::lexical_cast<T>("155397926921764129586412153075574099601109247922558905818374286709640260695423396870480843150490968148047148588235083389"),
 752       boost::lexical_cast<T>("251439127540686683410355036436498964627214165334435973635196551498669275073731875734673432234676222479684794771243158018"),
 753       boost::lexical_cast<T>("406837054462450812996767189512073064228323413256994879453570838208309535769155272605154275385167190627731943359478241407"),
 754       boost::lexical_cast<T>("658276182003137496407122225948572028855537578591430853088767389706978810842887148339827707619843413107416738130721399425"),
 755       boost::lexical_cast<T>("1065113236465588309403889415460645093083860991848425732542338227915288346612042420944981983005010603735148681490199640832"),
 756       boost::lexical_cast<T>("1723389418468725805811011641409217121939398570439856585631105617622267157454929569284809690624854016842565419620921040257"),
 757       boost::lexical_cast<T>("2788502654934314115214901056869862215023259562288282318173443845537555504066971990229791673629864620577714101111120681089"),
 758       boost::lexical_cast<T>("4511892073403039921025912698279079336962658132728138903804549463159822661521901559514601364254718637420279520732041721346"),
 759       boost::lexical_cast<T>("7300394728337354036240813755148941551985917695016421221977993308697378165588873549744393037884583257997993621843162402435"),
 760       boost::lexical_cast<T>("11812286801740393957266726453428020888948575827744560125782542771857200827110775109258994402139301895418273142575204123781"),
 761       boost::lexical_cast<T>("19112681530077747993507540208576962440934493522760981347760536080554578992699648659003387440023885153416266764418366526216"),
 762       boost::lexical_cast<T>("30924968331818141950774266662004983329883069350505541473543078852411779819810423768262381842163187048834539906993570649997"),
 763       boost::lexical_cast<T>("50037649861895889944281806870581945770817562873266522821303614932966358812510072427265769282187072202250806671411937176213"),
 764       boost::lexical_cast<T>("80962618193714031895056073532586929100700632223772064294846693785378138632320496195528151124350259251085346578405507826210"),
 765       boost::lexical_cast<T>("131000268055609921839337880403168874871518195097038587116150308718344497444830568622793920406537331453336153249817445002423"),
 766       boost::lexical_cast<T>("211962886249323953734393953935755803972218827320810651410997002503722636077151064818322071530887590704421499828222952828633"),
 767       boost::lexical_cast<T>("342963154304933875573731834338924678843737022417849238527147311222067133521981633441115991937424922157757653078040397831056"),
 768       boost::lexical_cast<T>("554926040554257829308125788274680482815955849738659889938144313725789769599132698259438063468312512862179152906263350659689"),
 769       boost::lexical_cast<T>("897889194859191704881857622613605161659692872156509128465291624947856903121114331700554055405737435019936805984303748490745"),
 770       boost::lexical_cast<T>("1452815235413449534189983410888285644475648721895169018403435938673646672720247029959992118874049947882115958890567099150434"),
 771       boost::lexical_cast<T>("2350704430272641239071841033501890806135341594051678146868727563621503575841361361660546174279787382902052764874870847641179"),
 772       boost::lexical_cast<T>("3803519665686090773261824444390176450610990315946847165272163502295150248561608391620538293153837330784168723765437946791613"),
 773       boost::lexical_cast<T>("6154224095958732012333665477892067256746331909998525312140891065916653824402969753281084467433624713686221488640308794432792"),
 774       boost::lexical_cast<T>("9957743761644822785595489922282243707357322225945372477413054568211804072964578144901622760587462044470390212405746741224405"),
 775       boost::lexical_cast<T>("16111967857603554797929155400174310964103654135943897789553945634128457897367547898182707228021086758156611701046055535657197"),
 776       boost::lexical_cast<T>("26069711619248377583524645322456554671460976361889270266967000202340261970332126043084329988608548802627001913451802276881602"),
 777       boost::lexical_cast<T>("42181679476851932381453800722630865635564630497833168056520945836468719867699673941267037216629635560783613614497857812538799"),
 778       boost::lexical_cast<T>("68251391096100309964978446045087420307025606859722438323487946038808981838031799984351367205238184363410615527949660089420401"),
 779       boost::lexical_cast<T>("110433070572952242346432246767718285942590237357555606380008891875277701705731473925618404421867819924194229142447517901959200"),
 780       boost::lexical_cast<T>("178684461669052552311410692812805706249615844217278044703496837914086683543763273909969771627106004287604844670397177991379601"),
 781       boost::lexical_cast<T>("289117532242004794657842939580523992192206081574833651083505729789364385249494747835588176048973824211799073812844695893338801"),
 782       boost::lexical_cast<T>("467801993911057346969253632393329698441821925792111695787002567703451068793258021745557947676079828499403918483241873884718402"),
 783       boost::lexical_cast<T>("756919526153062141627096571973853690634028007366945346870508297492815454042752769581146123725053652711202992296086569778057203"),
 784       boost::lexical_cast<T>("1224721520064119488596350204367183389075849933159057042657510865196266522836010791326704071401133481210606910779328443662775605"),
 785       boost::lexical_cast<T>("1981641046217181630223446776341037079709877940526002389528019162689081976878763560907850195126187133921809903075415013440832808"),
 786       boost::lexical_cast<T>("3206362566281301118819796980708220468785727873685059432185530027885348499714774352234554266527320615132416813854743457103608413"),
 787       boost::lexical_cast<T>("5188003612498482749043243757049257548495605814211061821713549190574430476593537913142404461653507749054226716930158470544441221"),
 788       boost::lexical_cast<T>("8394366178779783867863040737757478017281333687896121253899079218459778976308312265376958728180828364186643530784901927648049634"),
 789       boost::lexical_cast<T>("13582369791278266616906284494806735565776939502107183075612628409034209452901850178519363189834336113240870247715060398192490855"),
 790       boost::lexical_cast<T>("21976735970058050484769325232564213583058273190003304329511707627493988429210162443896321918015164477427513778499962325840540489"),
 791       boost::lexical_cast<T>("35559105761336317101675609727370949148835212692110487405124336036528197882112012622415685107849500590668384026215022724033031344"),
 792       boost::lexical_cast<T>("57535841731394367586444934959935162731893485882113791734636043664022186311322175066312007025864665068095897804714985049873571833"),
 793       boost::lexical_cast<T>("93094947492730684688120544687306111880728698574224279139760379700550384193434187688727692133714165658764281830930007773906603177"),
 794       boost::lexical_cast<T>("150630789224125052274565479647241274612622184456338070874396423364572570504756362755039699159578830726860179635644992823780175010"),
 795       boost::lexical_cast<T>("243725736716855736962686024334547386493350883030562350014156803065122954698190550443767391293292996385624461466575000597686778187"),
 796       boost::lexical_cast<T>("394356525940980789237251503981788661105973067486900420888553226429695525202946913198807090452871827112484641102219993421466953197"),
 797       boost::lexical_cast<T>("638082262657836526199937528316336047599323950517462770902710029494818479901137463642574481746164823498109102568794994019153731384"),
 798       boost::lexical_cast<T>("1032438788598817315437189032298124708705297018004363191791263255924514005104084376841381572199036650610593743671014987440620684581"),
 799       boost::lexical_cast<T>("1670521051256653841637126560614460756304620968521825962693973285419332485005221840483956053945201474108702846239809981459774415965"),
 800       boost::lexical_cast<T>("2702959839855471157074315592912585465009917986526189154485236541343846490109306217325337626144238124719296589910824968900395100546"),
 801       boost::lexical_cast<T>("4373480891112124998711442153527046221314538955048015117179209826763178975114528057809293680089439598827999436150634950360169516511"),
 802       boost::lexical_cast<T>("7076440730967596155785757746439631686324456941574204271664446368107025465223834275134631306233677723547296026061459919260564617057"),
 803       boost::lexical_cast<T>("11449921622079721154497199899966677907638995896622219388843656194870204440338362332943924986323117322375295462212094869620734133568"),
 804       boost::lexical_cast<T>("18526362353047317310282957646406309593963452838196423660508102562977229905562196608078556292556795045922591488273554788881298750625"),
 805       boost::lexical_cast<T>("29976283975127038464780157546372987501602448734818643049351758757847434345900558941022481278879912368297886950485649658502032884193"),
 806       boost::lexical_cast<T>("48502646328174355775063115192779297095565901573015066709859861320824664251462755549101037571436707414220478438759204447383331634818"),
 807       boost::lexical_cast<T>("78478930303301394239843272739152284597168350307833709759211620078672098597363314490123518850316619782518365389244854105885364519011"),
 808       boost::lexical_cast<T>("126981576631475750014906387931931581692734251880848776469071481399496762848826070039224556421753327196738843828004058553268696153829"),
 809       boost::lexical_cast<T>("205460506934777144254749660671083866289902602188682486228283101478168861446189384529348075272069946979257209217248912659154060672840"),
 810       boost::lexical_cast<T>("332442083566252894269656048603015447982636854069531262697354582877665624295015454568572631693823274175996053045252971212422756826669"),
 811       boost::lexical_cast<T>("537902590501030038524405709274099314272539456258213748925637684355834485741204839097920706965893221155253262262501883871576817499509"),
 812       boost::lexical_cast<T>("870344674067282932794061757877114762255176310327745011622992267233500110036220293666493338659716495331249315307754855083999574326178"),
 813       boost::lexical_cast<T>("1408247264568312971318467467151214076527715766585958760548629951589334595777425132764414045625609716486502577570256738955576391825687"),
 814       boost::lexical_cast<T>("2278591938635595904112529225028328838782892076913703772171622218822834705813645426430907384285326211817751892878011594039575966151865"),
 815       boost::lexical_cast<T>("3686839203203908875430996692179542915310607843499662532720252170412169301591070559195321429910935928304254470448268332995152357977552"),
 816       boost::lexical_cast<T>("5965431141839504779543525917207871754093499920413366304891874389235004007404715985626228814196262140122006363326279927034728324129417"),
 817       boost::lexical_cast<T>("9652270345043413654974522609387414669404107763913028837612126559647173308995786544821550244107198068426260833774548260029880682106969"),
 818       boost::lexical_cast<T>("15617701486882918434518048526595286423497607684326395142504000948882177316400502530447779058303460208548267197100828187064609006236386"),
 819       boost::lexical_cast<T>("25269971831926332089492571135982701092901715448239423980116127508529350625396289075269329302410658276974528030875376447094489688343355"),
 820       boost::lexical_cast<T>("40887673318809250524010619662577987516399323132565819122620128457411527941796791605717108360714118485522795227976204634159098694579741"),
 821       boost::lexical_cast<T>("66157645150735582613503190798560688609301038580805243102736255965940878567193080680986437663124776762497323258851581081253588382923096"),
 822       boost::lexical_cast<T>("107045318469544833137513810461138676125700361713371062225356384423352406508989872286703546023838895248020118486827785715412687077502837"),
 823       boost::lexical_cast<T>("173202963620280415751017001259699364735001400294176305328092640389293285076182952967689983686963672010517441745679366796666275460425933"),
 824       boost::lexical_cast<T>("280248282089825248888530811720838040860701762007547367553449024812645691585172825254393529710802567258537560232507152512078962537928770"),
 825       boost::lexical_cast<T>("453451245710105664639547812980537405595703162301723672881541665201938976661355778222083513397766239269055001978186519308745237998354703"),
 826       boost::lexical_cast<T>("733699527799930913528078624701375446456404924309271040434990690014584668246528603476477043108568806527592562210693671820824200536283473"),
 827       boost::lexical_cast<T>("1187150773510036578167626437681912852052108086610994713316532355216523644907884381698560556506335045796647564188880191129569438534638176"),
 828       boost::lexical_cast<T>("1920850301309967491695705062383288298508513010920265753751523045231108313154412985175037599614903852324240126399573862950393639070921649"),
 829       boost::lexical_cast<T>("3108001074820004069863331500065201150560621097531260467068055400447631958062297366873598156121238898120887690588454054079963077605559825"),
 830       boost::lexical_cast<T>("5028851376129971561559036562448489449069134108451526220819578445678740271216710352048635755736142750445127816988027917030356716676481474"),
 831       boost::lexical_cast<T>("8136852450949975631422368062513690599629755205982786687887633846126372229279007718922233911857381648566015507576481971110319794282041299"),
 832       boost::lexical_cast<T>("13165703827079947192981404624962180048698889314434312908707212291805112500495718070970869667593524399011143324564509888140676510958522773"),
 833       boost::lexical_cast<T>("21302556278029922824403772687475870648328644520417099596594846137931484729774725789893103579450906047577158832140991859250996305240564072"),
 834       boost::lexical_cast<T>("34468260105109870017385177312438050697027533834851412505302058429736597230270443860863973247044430446588302156705501747391672816199086845"),
 835       boost::lexical_cast<T>("55770816383139792841788949999913921345356178355268512101896904567668081960045169650757076826495336494165460988846493606642669121439650917"),
 836       boost::lexical_cast<T>("90239076488249662859174127312351972042383712190119924607198962997404679190315613511621050073539766940753763145551995354034341937638737762"),
 837       boost::lexical_cast<T>("146009892871389455700963077312265893387739890545388436709095867565072761150360783162378126900035103434919224134398488960677011059078388679"),
 838       boost::lexical_cast<T>("236248969359639118560137204624617865430123602735508361316294830562477440340676396673999176973574870375672987279950484314711352996717126441"),
 839       boost::lexical_cast<T>("382258862231028574261100281936883758817863493280896798025390698127550201491037179836377303873609973810592211414348973275388364055795515120"),
 840       boost::lexical_cast<T>("618507831590667692821237486561501624247987096016405159341685528690027641831713576510376480847184844186265198694299457590099717052512641561"),
 841       boost::lexical_cast<T>("1000766693821696267082337768498385383065850589297301957367076226817577843322750756346753784720794817996857410108648430865488081108308156681"),
 842       boost::lexical_cast<T>("1619274525412363959903575255059887007313837685313707116708761755507605485154464332857130265567979662183122608802947888455587798160820798242"),
 843       boost::lexical_cast<T>("2620041219234060226985913023558272390379688274611009074075837982325183328477215089203884050288774480179980018911596319321075879269128954923"),
 844       boost::lexical_cast<T>("4239315744646424186889488278618159397693525959924716190784599737832788813631679422061014315856754142363102627714544207776663677429949753165"),
 845       boost::lexical_cast<T>("6859356963880484413875401302176431788073214234535725264860437720157972142108894511264898366145528622543082646626140527097739556699078708088"),
 846       boost::lexical_cast<T>("11098672708526908600764889580794591185766740194460441455645037457990760955740573933325912682002282764906185274340684734874403234129028461253"),
 847       boost::lexical_cast<T>("17958029672407393014640290882971022973839954428996166720505475178148733097849468444590811048147811387449267920966825261972142790828107169341"),
 848       boost::lexical_cast<T>("29056702380934301615405180463765614159606694623456608176150512636139494053590042377916723730150094152355453195307509996846546024957135630594"),
 849       boost::lexical_cast<T>("47014732053341694630045471346736637133446649052452774896655987814288227151439510822507534778297905539804721116274335258818688815785242799935"),
 850       boost::lexical_cast<T>("76071434434275996245450651810502251293053343675909383072806500450427721205029553200424258508447999692160174311581845255665234840742378430529"),
 851       boost::lexical_cast<T>("123086166487617690875496123157238888426499992728362157969462488264715948356469064022931793286745905231964895427856180514483923656527621230464"),
 852       boost::lexical_cast<T>("199157600921893687120946774967741139719553336404271541042268988715143669561498617223356051795193904924125069739438025770149158497269999660993"),
 853       boost::lexical_cast<T>("322243767409511377996442898124980028146053329132633699011731476979859617917967681246287845081939810156089965167294206284633082153797620891457"),
 854       boost::lexical_cast<T>("521401368331405065117389673092721167865606665536905240054000465695003287479466298469643896877133715080215034906732232054782240651067620552450"),
 855       boost::lexical_cast<T>("843645135740916443113832571217701196011659994669538939065731942674862905397433979715931741959073525236305000074026438339415322804865241443907"),
 856       boost::lexical_cast<T>("1365046504072321508231222244310422363877266660206444179119732408369866192876900278185575638836207240316520034980758670394197563455932861996357"),
 857       boost::lexical_cast<T>("2208691639813237951345054815528123559888926654875983118185464351044729098274334257901507380795280765552825035054785108733612886260798103440264"),
 858       boost::lexical_cast<T>("3573738143885559459576277059838545923766193315082427297305196759414595291151234536087083019631488005869345070035543779127810449716730965436621"),
 859       boost::lexical_cast<T>("5782429783698797410921331875366669483655119969958410415490661110459324389425568793988590400426768771422170105090328887861423335977529068876885"),
 860       boost::lexical_cast<T>("9356167927584356870497608935205215407421313285040837712795857869873919680576803330075673420058256777291515175125872666989233785694260034313506"),
 861       boost::lexical_cast<T>("15138597711283154281418940810571884891076433254999248128286518980333244070002372124064263820485025548713685280216201554850657121671789103190391"),
 862       boost::lexical_cast<T>("24494765638867511151916549745777100298497746540040085841082376850207163750579175454139937240543282326005200455342074221839890907366049137503897"),
 863       boost::lexical_cast<T>("39633363350150665433335490556348985189574179795039333969368895830540407820581547578204201061028307874718885735558275776690548029037838240694288"),
 864       boost::lexical_cast<T>("64128128989018176585252040302126085488071926335079419810451272680747571571160723032344138301571590200724086190900349998530438936403887378198185"),
 865       boost::lexical_cast<T>("103761492339168842018587530858475070677646106130118753779820168511287979391742270610548339362599898075442971926458625775220986965441725618892473"),
 866       boost::lexical_cast<T>("167889621328187018603839571160601156165718032465198173590271441192035550962902993642892477664171488276167058117358975773751425901845612997090658"),
 867       boost::lexical_cast<T>("271651113667355860622427102019076226843364138595316927370091609703323530354645264253440817026771386351610030043817601548972412867287338615983131"),
 868       boost::lexical_cast<T>("439540734995542879226266673179677383009082171060515100960363050895359081317548257896333294690942874627777088161176577322723838769132951613073789"),
 869       boost::lexical_cast<T>("711191848662898739848693775198753609852446309655832028330454660598682611672193522149774111717714260979387118204994178871696251636420290229056920"),
 870       boost::lexical_cast<T>("1150732583658441619074960448378430992861528480716347129290817711494041692989741780046107406408657135607164206366170756194420090405553241842130709"),
 871       boost::lexical_cast<T>("1861924432321340358923654223577184602713974790372179157621272372092724304661935302195881518126371396586551324571164935066116342041973532071187629"),
 872       boost::lexical_cast<T>("3012657015979781977998614671955615595575503271088526286912090083586765997651677082241988924535028532193715530937335691260536432447526773913318338"),
 873       boost::lexical_cast<T>("4874581448301122336922268895532800198289478061460705444533362455679490302313612384437870442661399928780266855508500626326652774489500305984505967"),
 874       boost::lexical_cast<T>("7887238464280904314920883567488415793864981332549231731445452539266256299965289466679859367196428460973982386445836317587189206937027079897824305"),
 875       boost::lexical_cast<T>("12761819912582026651843152463021215992154459394009937175978814994945746602278901851117729809857828389754249241954336943913841981426527385882330272"),
 876       boost::lexical_cast<T>("20649058376862930966764036030509631786019440726559168907424267534212002902244191317797589177054256850728231628400173261501031188363554465780154577"),
 877       boost::lexical_cast<T>("33410878289444957618607188493530847778173900120569106083403082529157749504523093168915318986912085240482480870354510205414873169790081851662484849"),
 878       boost::lexical_cast<T>("54059936666307888585371224524040479564193340847128274990827350063369752406767284486712908163966342091210712498754683466915904358153636317442639426"),
 879       boost::lexical_cast<T>("87470814955752846203978413017571327342367240967697381074230432592527501911290377655628227150878427331693193369109193672330777527943718169105124275"),
 880       boost::lexical_cast<T>("141530751622060734789349637541611806906560581814825656065057782655897254318057662142341135314844769422903905867863877139246681886097354486547763701"),
 881       boost::lexical_cast<T>("229001566577813580993328050559183134248927822782523037139288215248424756229348039797969362465723196754597099236973070811577459414041072655652887976"),
 882       boost::lexical_cast<T>("370532318199874315782677688100794941155488404597348693204345997904322010547405701940310497780567966177501005104836947950824141300138427142200651677"),
 883       boost::lexical_cast<T>("599533884777687896776005738659978075404416227379871730343634213152746766776753741738279860246291162932098104341810018762401600714179499797853539653"),
 884       boost::lexical_cast<T>("970066202977562212558683426760773016559904631977220423547980211057068777324159443678590358026859129109599109446646966713225742014317926940054191330"),
 885       boost::lexical_cast<T>("1569600087755250109334689165420751091964320859357092153891614424209815544100913185416870218273150292041697213788456985475627342728497426737907730983"),
 886       boost::lexical_cast<T>("2539666290732812321893372592181524108524225491334312577439594635266884321425072629095460576300009421151296323235103952188853084742815353677961922313"),
 887       boost::lexical_cast<T>("4109266378488062431228061757602275200488546350691404731331209059476699865525985814512330794573159713192993537023560937664480427471312780415869653296"),
 888       boost::lexical_cast<T>("6648932669220874753121434349783799309012771842025717308770803694743584186951058443607791370873169134344289860258664889853333512214128134093831575609"),
 889       boost::lexical_cast<T>("10758199047708937184349496107386074509501318192717122040102012754220284052477044258120122165446328847537283397282225827517813939685440914509701228905"),
 890       boost::lexical_cast<T>("17407131716929811937470930457169873818514090034742839348872816448963868239428102701727913536319497981881573257540890717371147451899569048603532804514"),
 891       boost::lexical_cast<T>("28165330764638749121820426564555948328015408227459961388974829203184152291905146959848035701765826829418856654823116544888961391585009963113234033419"),
 892       boost::lexical_cast<T>("45572462481568561059291357021725822146529498262202800737847645652148020531333249661575949238085324811300429912364007262260108843484579011716766837933"),
 893       boost::lexical_cast<T>("73737793246207310181111783586281770474544906489662762126822474855332172823238396621423984939851151640719286567187123807149070235069588974830000871352"),
 894       boost::lexical_cast<T>("119310255727775871240403140608007592621074404751865562864670120507480193354571646282999934177936476452019716479551131069409179078554167986546767709285"),
 895       boost::lexical_cast<T>("193048048973983181421514924194289363095619311241528324991492595362812366177810042904423919117787628092739003046738254876558249313623756961376768580637"),
 896       boost::lexical_cast<T>("312358304701759052661918064802296955716693715993393887856162715870292559532381689187423853295724104544758719526289385945967428392177924947923536289922"),
 897       boost::lexical_cast<T>("505406353675742234083432988996586318812313027234922212847655311233104925710191732091847772413511732637497722573027640822525677705801681909300304870559"),
 898       boost::lexical_cast<T>("817764658377501286745351053798883274529006743228316100703818027103397485242573421279271625709235837182256442099317026768493106097979606857223841160481"),
 899       boost::lexical_cast<T>("1323171012053243520828784042795469593341319770463238313551473338336502410952765153371119398122747569819754164672344667591018783803781288766524146031040"),
 900       boost::lexical_cast<T>("2140935670430744807574135096594352867870326513691554414255291365439899896195338574650391023831983407002010606771661694359511889901760895623747987191521"),
 901       boost::lexical_cast<T>("3464106682483988328402919139389822461211646284154792727806764703776402307148103728021510421954730976821764771444006361950530673705542184390272133222561"),
 902       boost::lexical_cast<T>("5605042352914733135977054235984175329081972797846347142062056069216302203343442302671901445786714383823775378215668056310042563607303080014020120414082"),
 903       boost::lexical_cast<T>("9069149035398721464379973375373997790293619082001139869868820772992704510491546030693411867741445360645540149659674418260573237312845264404292253636643"),
 904       boost::lexical_cast<T>("14674191388313454600357027611358173119375591879847487011930876842209006713834988333365313313528159744469315527875342474570615800920148344418312374050725"),
 905       boost::lexical_cast<T>("23743340423712176064737000986732170909669210961848626881799697615201711224326534364058725181269605105114855677535016892831189038232993608822604627687368"),
 906       boost::lexical_cast<T>("38417531812025630665094028598090344029044802841696113893730574457410717938161522697424038494797764849584171205410359367401804839153141953240917001738093"),
 907       boost::lexical_cast<T>("62160872235737806729831029584822514938714013803544740775530272072612429162488057061482763676067369954699026882945376260232993877386135562063521629425461"),
 908       boost::lexical_cast<T>("100578404047763437394925058182912858967758816645240854669260846530023147100649579758906802170865134804283198088355735627634798716539277515304438631163554"),
 909       boost::lexical_cast<T>("162739276283501244124756087767735373906472830448785595444791118602635576263137636820389565846932504758982224971301111887867792593925413077367960260589015"),
 910       boost::lexical_cast<T>("263317680331264681519681145950648232874231647094026450114051965132658723363787216579296368017797639563265423059656847515502591310464690592672398891752569"),
 911       boost::lexical_cast<T>("426056956614765925644437233718383606780704477542812045558843083735294299626924853399685933864730144322247648030957959403370383904390103670040359152341584"),
 912       boost::lexical_cast<T>("689374636946030607164118379669031839654936124636838495672895048867953022990712069978982301882527783885513071090614806918872975214854794262712758044094153"),
 913       boost::lexical_cast<T>("1115431593560796532808555613387415446435640602179650541231738132603247322617636923378668235747257928207760719121572766322243359119244897932753117196435737"),
 914       boost::lexical_cast<T>("1804806230506827139972673993056447286090576726816489036904633181471200345608348993357650537629785712093273790212187573241116334334099692195465875240529890"),
 915       boost::lexical_cast<T>("2920237824067623672781229606443862732526217328996139578136371314074447668225985916736318773377043640301034509333760339563359693453344590128218992436965627"),
 916       boost::lexical_cast<T>("4725044054574450812753903599500310018616794055812628615041004495545648013834334910093969311006829352394308299545947912804476027787444282323684867677495517"),
 917       boost::lexical_cast<T>("7645281878642074485535133205944172751143011384808768193177375809620095682060320826830288084383872992695342808879708252367835721240788872451903860114461144"),
 918       boost::lexical_cast<T>("12370325933216525298289036805444482769759805440621396808218380305165743695894655736924257395390702345089651108425656165172311749028233154775588727791956661"),
 919       boost::lexical_cast<T>("20015607811858599783824170011388655520902816825430165001395756114785839377954976563754545479774575337784993917305364417540147470269022027227492587906417805"),
 920       boost::lexical_cast<T>("32385933745075125082113206816833138290662622266051561809614136419951583073849632300678802875165277682874645025731020582712459219297255182003081315698374466"),
 921       boost::lexical_cast<T>("52401541556933724865937376828221793811565439091481726811009892534737422451804608864433348354939853020659638943036385000252606689566277209230573903604792271"),
 922       boost::lexical_cast<T>("84787475302008849948050583645054932102228061357533288620624028954689005525654241165112151230105130703534283968767405582965065908863532391233655219303166737"),
 923       boost::lexical_cast<T>("137189016858942574813987960473276725913793500449015015431633921489426427977458850029545499585044983724193922911803790583217672598429809600464229122907959008"),
 924       boost::lexical_cast<T>("221976492160951424762038544118331658016021561806548304052257950444115433503113091194657650815150114427728206880571196166182738507293341991697884342211125745"),
 925       boost::lexical_cast<T>("359165509019893999576026504591608383929815062255563319483891871933541861480571941224203150400195098151922129792374986749400411105723151592162113465119084753"),
 926       boost::lexical_cast<T>("581142001180845424338065048709940041945836624062111623536149822377657294983685032418860801215345212579650336672946182915583149613016493583859997807330210498"),
 927       boost::lexical_cast<T>("940307510200739423914091553301548425875651686317674943020041694311199156464256973643063951615540310731572466465321169664983560718739645176022111272449295251"),
 928       boost::lexical_cast<T>("1521449511381584848252156602011488467821488310379786566556191516688856451447942006061924752830885523311222803138267352580566710331756138759882109079779505749"),
 929       boost::lexical_cast<T>("2461757021582324272166248155313036893697139996697461509576233211000055607912198979704988704446425834042795269603588522245550271050495783935904220352228801000"),
 930       boost::lexical_cast<T>("3983206532963909120418404757324525361518628307077248076132424727688912059360140985766913457277311357354018072741855874826116981382251922695786329432008306749"),
 931       boost::lexical_cast<T>("6444963554546233392584652912637562255215768303774709585708657938688967667272339965471902161723737191396813342345444397071667252432747706631690549784237107749"),
 932       boost::lexical_cast<T>("10428170087510142513003057669962087616734396610851957661841082666377879726632480951238815619001048548750831415087300271897784233814999629327476879216245414498"),
 933       boost::lexical_cast<T>("16873133642056375905587710582599649871950164914626667247549740605066847393904820916710717780724785740147644757432744668969451486247747335959167429000482522247"),
 934       boost::lexical_cast<T>("27301303729566518418590768252561737488684561525478624909390823271444727120537301867949533399725834288898476172520044940867235720062746965286644308216727936745"),
 935       boost::lexical_cast<T>("44174437371622894324178478835161387360634726440105292156940563876511574514442122784660251180450620029046120929952789609836687206310494301245811737217210458992"),
 936       boost::lexical_cast<T>("71475741101189412742769247087723124849319287965583917066331387147956301634979424652609784580176454317944597102472834550703922926373241266532456045433938395737"),
 937       boost::lexical_cast<T>("115650178472812307066947725922884512209954014405689209223271951024467876149421547437270035760627074346990718032425624160540610132683735567778267782651148854729"),
 938       boost::lexical_cast<T>("187125919574001719809716973010607637059273302371273126289603338172424177784400972089879820340803528664935315134898458711244533059056976834310723828085087250466"),
 939       boost::lexical_cast<T>("302776098046814026876664698933492149269227316776962335512875289196892053933822519527149856101430603011926033167324082871785143191740712402088991610736236105195"),
 940       boost::lexical_cast<T>("489902017620815746686381671944099786328500619148235461802478627369316231718223491617029676442234131676861348302222541583029676250797689236399715438821323355661"),
 941       boost::lexical_cast<T>("792678115667629773563046370877591935597727935925197797315353916566208285652046011144179532543664734688787381469546624454814819442538401638488707049557559460856"),
 942       boost::lexical_cast<T>("1282580133288445520249428042821691721926228555073433259117832543935524517370269502761209208985898866365648729771769166037844495693336090874888422488378882816517"),
 943       boost::lexical_cast<T>("2075258248956075293812474413699283657523956490998631056433186460501732803022315513905388741529563601054436111241315790492659315135874492513377129537936442277373"),
 944       boost::lexical_cast<T>("3357838382244520814061902456520975379450185046072064315551019004437257320392585016666597950515462467420084841013084956530503810829210583388265552026315325093890"),
 945       boost::lexical_cast<T>("5433096631200596107874376870220259036974141537070695371984205464938990123414900530571986692045026068474520952254400747023163125965085075901642681564251767371263"),
 946       boost::lexical_cast<T>("8790935013445116921936279326741234416424326583142759687535224469376247443807485547238584642560488535894605793267485703553666936794295659289908233590567092465153"),
 947       boost::lexical_cast<T>("14224031644645713029810656196961493453398468120213455059519429934315237567222386077810571334605514604369126745521886450576830062759380735191550915154818859836416"),
 948       boost::lexical_cast<T>("23014966658090829951746935523702727869822794703356214747054654403691485011029871625049155977166003140263732538789372154130496999553676394481459148745385952301569"),
 949       boost::lexical_cast<T>("37238998302736542981557591720664221323221262823569669806574084338006722578252257702859727311771517744632859284311258604707327062313057129673010063900204812137985"),
 950       boost::lexical_cast<T>("60253964960827372933304527244366949193044057526925884553628738741698207589282129327908883288937520884896591823100630758837824061866733524154469212645590764439554"),
 951       boost::lexical_cast<T>("97492963263563915914862118965031170516265320350495554360202823079704930167534387030768610600709038629529451107411889363545151124179790653827479276545795576577539"),
 952       boost::lexical_cast<T>("157746928224391288848166646209398119709309377877421438913831561821403137756816516358677493889646559514426042930512520122382975186046524177981948489191386341017093"),
 953       boost::lexical_cast<T>("255239891487955204763028765174429290225574698227916993274034384901108067924350903389446104490355598143955494037924409485928126310226314831809427765737181917594632"),
 954       boost::lexical_cast<T>("412986819712346493611195411383827409934884076105338432187865946722511205681167419748123598380002157658381536968436929608311101496272839009791376254928568258611725"),
 955       boost::lexical_cast<T>("668226711200301698374224176558256700160458774333255425461900331623619273605518323137569702870357755802337031006361339094239227806499153841600804020665750176206357"),
 956       boost::lexical_cast<T>("1081213530912648191985419587942084110095342850438593857649766278346130479286685742885693301250359913460718567974798268702550329302771992851392180275594318434818082"),
 957       boost::lexical_cast<T>("1749440242112949890359643764500340810255801624771849283111666609969749752892204066023263004120717669263055598981159607796789557109271146692992984296260068611024439"),
 958       boost::lexical_cast<T>("2830653773025598082345063352442424920351144475210443140761432888315880232178889808908956305371077582723774166955957876499339886412043139544385164571854387045842521"),
 959       boost::lexical_cast<T>("4580094015138547972704707116942765730606946099982292423873099498285629985071093874932219309491795251986829765937117484296129443521314286237378148868114455656866960"),
 960       boost::lexical_cast<T>("7410747788164146055049770469385190650958090575192735564634532386601510217249983683841175614862872834710603932893075360795469329933357425781763313439968842702709481"),
 961       boost::lexical_cast<T>("11990841803302694027754477586327956381565036675175027988507631884887140202321077558773394924354668086697433698830192845091598773454671712019141462308083298359576441"),
 962       boost::lexical_cast<T>("19401589591466840082804248055713147032523127250367763553142164271488650419571061242614570539217540921408037631723268205887068103388029137800904775748052141062285922"),
 963       boost::lexical_cast<T>("31392431394769534110558725642041103414088163925542791541649796156375790621892138801387965463572209008105471330553461050978666876842700849820046238056135439421862363"),
 964       boost::lexical_cast<T>("50794020986236374193362973697754250446611291175910555094791960427864441041463200044002536002789749929513508962276729256865734980230729987620951013804187580484148285"),
 965       boost::lexical_cast<T>("82186452381005908303921699339795353860699455101453346636441756584240231663355338845390501466361958937618980292830190307844401857073430837440997251860323019906010648"),
 966       boost::lexical_cast<T>("132980473367242282497284673037549604307310746277363901731233717012104672704818538889393037469151708867132489255106919564710136837304160825061948265664510600390158933"),
 967       boost::lexical_cast<T>("215166925748248190801206372377344958168010201378817248367675473596344904368173877734783538935513667804751469547937109872554538694377591662502945517524833620296169581"),
 968       boost::lexical_cast<T>("348147399115490473298491045414894562475320947656181150098909190608449577072992416624176576404665376671883958803044029437264675531681752487564893783189344220686328514"),
 969       boost::lexical_cast<T>("563314324863738664099697417792239520643331149034998398466584664204794481441166294358960115340179044476635428350981139309819214226059344150067839300714177840982498095"),
 970       boost::lexical_cast<T>("911461723979229137398188463207134083118652096691179548565493854813244058514158710983136691744844421148519387154025168747083889757741096637632733083903522061668826609"),
 971       boost::lexical_cast<T>("1474776048842967801497885880999373603761983245726177947032078519018038539955325005342096807085023465625154815505006308056903103983800440787700572384617699902651324704"),
 972       boost::lexical_cast<T>("2386237772822196938896074344206507686880635342417357495597572373831282598469483716325233498829867886773674202659031476803986993741541537425333305468521221964320151313"),
 973       boost::lexical_cast<T>("3861013821665164740393960225205881290642618588143535442629650892849321138424808721667330305914891352398829018164037784860890097725341978213033877853138921866971476017"),
 974       boost::lexical_cast<T>("6247251594487361679290034569412388977523253930560892938227223266680603736894292437992563804744759239172503220823069261664877091466883515638367183321660143831291627330"),
 975       boost::lexical_cast<T>("10108265416152526419683994794618270268165872518704428380856874159529924875319101159659894110659650591571332238987107046525767189192225493851401061174799065698263103347"),
 976       boost::lexical_cast<T>("16355517010639888098974029364030659245689126449265321319084097426210528612213393597652457915404409830743835459810176308190644280659109009489768244496459209529554730677"),
 977       boost::lexical_cast<T>("26463782426792414518658024158648929513854998967969749699940971585740453487532494757312352026064060422315167698797283354716411469851334503341169305671258275227817834024"),
 978       boost::lexical_cast<T>("42819299437432302617632053522679588759544125417235071019025069011950982099745888354964809941468470253059003158607459662907055750510443512830937550167717484757372564701"),
 979       boost::lexical_cast<T>("69283081864224717136290077681328518273399124385204820718966040597691435587278383112277161967532530675374170857404743017623467220361778016172106855838975759985190398725"),
 980       boost::lexical_cast<T>("112102381301657019753922131204008107032943249802439891737991109609642417687024271467241971909001000928433174016012202680530522970872221529003044406006693244742562963426"),
 981       boost::lexical_cast<T>("181385463165881736890212208885336625306342374187644712456957150207333853274302654579519133876533531603807344873416945698153990191233999545175151261845669004727753362151"),
 982       boost::lexical_cast<T>("293487844467538756644134340089344732339285623990084604194948259816976270961326926046761105785534532532240518889429148378684513162106221074178195667852362249470316325577"),
 983       boost::lexical_cast<T>("474873307633420493534346548974681357645627998177729316651905410024310124235629580626280239662068064136047863762846094076838503353340220619353346929698031254198069687728"),
 984       boost::lexical_cast<T>("768361152100959250178480889064026089984913622167813920846853669841286395196956506673041345447602596668288382652275242455523016515446441693531542597550393503668386013305"),
 985       boost::lexical_cast<T>("1243234459734379743712827438038707447630541620345543237498759079865596519432586087299321585109670660804336246415121336532361519868786662312884889527248424757866455701033"),
 986       boost::lexical_cast<T>("2011595611835338993891308327102733537615455242513357158345612749706882914629542593972362930557273257472624629067396578987884536384233104006416432124798818261534841714338"),
 987       boost::lexical_cast<T>("3254830071569718737604135765141440985245996862858900395844371829572479434062128681271684515666943918276960875482517915520246056253019766319301321652047243019401297415371"),
 988       boost::lexical_cast<T>("5266425683405057731495444092244174522861452105372257554189984579279362348691671275244047446224217175749585504549914494508130592637252870325717753776846061280936139129709"),
 989       boost::lexical_cast<T>("8521255754974776469099579857385615508107448968231157950034356408851841782753799956515731961891161094026546380032432410028376648890272636645019075428893304300337436545080"),
 990       boost::lexical_cast<T>("13787681438379834200595023949629790030968901073603415504224340988131204131445471231759779408115378269776131884582346904536507241527525506970736829205739365581273575674789"),
 991       boost::lexical_cast<T>("22308937193354610669694603807015405539076350041834573454258697396983045914199271188275511370006539363802678264614779314564883890417798143615755904634632669881611012219869"),
 992       boost::lexical_cast<T>("36096618631734444870289627756645195570045251115437988958483038385114250045644742420035290778121917633578810149197126219101391131945323650586492733840372035462884587894658"),
 993       boost::lexical_cast<T>("58405555825089055539984231563660601109121601157272562412741735782097295959844013608310802148128456997381488413811905533666275022363121794202248638475004705344495600114527"),
 994       boost::lexical_cast<T>("94502174456823500410273859320305796679166852272710551371224774167211546005488756028346092926250374630960298563009031752767666154308445444788741372315376740807380188009185"),
 995       boost::lexical_cast<T>("152907730281912555950258090883966397788288453429983113783966509949308841965332769636656895074378831628341786976820937286433941176671567238990990010790381446151875788123712"),
 996       boost::lexical_cast<T>("247409904738736056360531950204272194467455305702693665155191284116520387970821525665002988000629206259302085539829969039201607330980012683779731383105758186959255976132897"),
 997       boost::lexical_cast<T>("400317635020648612310790041088238592255743759132676778939157794065829229936154295301659883075008037887643872516650906325635548507651579922770721393896139633111131764256609"),
 998       boost::lexical_cast<T>("647727539759384668671321991292510786723199064835370444094349078182349617906975820966662871075637244146945958056480875364837155838631592606550452777001897820070387740389506"),
 999       boost::lexical_cast<T>("1048045174780033280982112032380749378978942823968047223033506872248178847843130116268322754150645282034589830573131781690472704346283172529321174170898037453181519504646115"),
1000       boost::lexical_cast<T>("1695772714539417949653434023673260165702141888803417667127855950430528465750105937234985625226282526181535788629612657055309860184914765135871626947899935273251907245035621"),
1001       boost::lexical_cast<T>("2743817889319451230635546056054009544681084712771464890161362822678707313593236053503308379376927808216125619202744438745782564531197937665192801118797972726433426749681736"),
1002       boost::lexical_cast<T>("4439590603858869180288980079727269710383226601574882557289218773109235779343341990738294004603210334397661407832357095801092424716112702801064428066697907999685333994717357"),
1003       boost::lexical_cast<T>("7183408493178320410924526135781279255064311314346347447450581595787943092936578044241602383980138142613787027035101534546874989247310640466257229185495880726118760744399093"),
1004       boost::lexical_cast<T>("11622999097037189591213506215508548965447537915921230004739800368897178872279920034979896388583348477011448434867458630347967413963423343267321657252193788725804094739116450"),
1005       boost::lexical_cast<T>("18806407590215510002138032351289828220511849230267577452190381964685121965216498079221498772563486619625235461902560164894842403210733983733578886437689669451922855483515543"),
1006       boost::lexical_cast<T>("30429406687252699593351538566798377185959387146188807456930182333582300837496418114201395161146835096636683896770018795242809817174157327000900543689883458177726950222631993"),
1007       boost::lexical_cast<T>("49235814277468209595489570918088205406471236376456384909120564298267422802712916193422893933710321716261919358672578960137652220384891310734479430127573127629649805706147536"),
1008       boost::lexical_cast<T>("79665220964720909188841109484886582592430623522645192366050746631849723640209334307624289094857156812898603255442597755380462037559048637735379973817456585807376755928779529"),
1009       boost::lexical_cast<T>("128901035242189118784330680402974787998901859899101577275171310930117146442922250501047183028567478529160522614115176715518114257943939948469859403945029713437026561634927065"),
1010       boost::lexical_cast<T>("208566256206910027973171789887861370591332483421746769641222057561966870083131584808671472123424635342059125869557774470898576295502988586205239377762486299244403317563706594"),
1011       boost::lexical_cast<T>("337467291449099146757502470290836158590234343320848346916393368492084016526053835309718655151992113871219648483672951186416690553446928534675098781707516012681429879198633659"),
1012       boost::lexical_cast<T>("546033547656009174730674260178697529181566826742595116557615426054050886609185420118390127275416749213278774353230725657315266848949917120880338159470002311925833196762340253"),
1013       boost::lexical_cast<T>("883500839105108321488176730469533687771801170063443463474008794546134903135239255428108782427408863084498422836903676843731957402396845655555436941177518324607263075960973912"),
1014       boost::lexical_cast<T>("1429534386761117496218850990648231216953367996806038580031624220600185789744424675546498909702825612297777197190134402501047224251346762776435775100647520636533096272723314165"),
1015       boost::lexical_cast<T>("2313035225866225817707027721117764904725169166869482043505633015146320692879663930974607692130234475382275620027038079344779181653743608431991212041825038961140359348684288077"),
1016       boost::lexical_cast<T>("3742569612627343313925878711765996121678537163675520623537257235746506482624088606521106601833060087680052817217172481845826405905090371208426987142472559597673455621407602242"),
1017       boost::lexical_cast<T>("6055604838493569131632906432883761026403706330545002667042890250892827175503752537495714293963294563062328437244210561190605587558833979640418199184297598558813814970091890319"),
1018       boost::lexical_cast<T>("9798174451120912445558785144649757148082243494220523290580147486639333658127841144016820895796354650742381254461383043036431993463924350848845186326770158156487270591499492561"),
1019       boost::lexical_cast<T>("15853779289614481577191691577533518174485949824765525957623037737532160833631593681512535189759649213804709691705593604227037581022758330489263385511067756715301085561591382880"),
1020       boost::lexical_cast<T>("25651953740735394022750476722183275322568193318986049248203185224171494491759434825529356085556003864547090946166976647263469574486682681338108571837837914871788356153090875441"),
1021       boost::lexical_cast<T>("41505733030349875599942168299716793497054143143751575205826222961703655325391028507041891275315653078351800637872570251490507155509441011827371957348905671587089441714682258321"),
1022       boost::lexical_cast<T>("67157686771085269622692645021900068819622336462737624454029408185875149817150463332571247360871656942898891584039546898753976729996123693165480529186743586458877797867773133762"),
1023       boost::lexical_cast<T>("108663419801435145222634813321616862316676479606489199659855631147578805142541491839613138636187310021250692221912117150244483885505564704992852486535649258045967239582455392083"),
1024       boost::lexical_cast<T>("175821106572520414845327458343516931136298816069226824113885039333453954959691955172184385997058966964149583805951664048998460615501688398158333015722392844504845037450228525845"),
1025       boost::lexical_cast<T>("284484526373955560067962271665133793452975295675716023773740670481032760102233447011797524633246276985400276027863781199242944501007253103151185502258042102550812277032683917928"),
1026       boost::lexical_cast<T>("460305632946475974913289730008650724589274111744942847887625709814486715061925402183981910630305243949549859833815445248241405116508941501309518517980434947055657314482912443773"),
1027       boost::lexical_cast<T>("744790159320431534981252001673784518042249407420658871661366380295519475164158849195779435263551520934950135861679226447484349617516194604460704020238477049606469591515596361701"),
1028       boost::lexical_cast<T>("1205095792266907509894541731682435242631523519165601719548992090110006190226084251379761345893856764884499995695494671695725754734025136105770222538218911996662126905998508805474"),
1029       boost::lexical_cast<T>("1949885951587339044875793733356219760673772926586260591210358470405525665390243100575540781157408285819450131557173898143210104351541330710230926558457389046268596497514105167175"),
1030       boost::lexical_cast<T>("3154981743854246554770335465038655003305296445751862310759350560515531855616327351955302127051265050703950127252668569838935859085566466816001149096676301042930723403512613972649"),
1031       boost::lexical_cast<T>("5104867695441585599646129198394874763979069372338122901969709030921057521006570452530842908208673336523400258809842467982145963437107797526232075655133690089199319901026719139824"),
1032       boost::lexical_cast<T>("8259849439295832154416464663433529767284365818089985212729059591436589376622897804486145035259938387227350386062511037821081822522674264342233224751809991132130043304539333112473"),
1033       boost::lexical_cast<T>("13364717134737417754062593861828404531263435190428108114698768622357646897629468257016987943468611723750750644872353505803227785959782061868465300406943681221329363205566052252297"),
1034       boost::lexical_cast<T>("21624566574033249908479058525261934298547801008518093327427828213794236274252366061503132978728550110978101030934864543624309608482456326210698525158753672353459406510105385364770"),
1035       boost::lexical_cast<T>("34989283708770667662541652387090338829811236198946201442126596836151883171881834318520120922197161834728851675807218049427537394442238388079163825565697353574788769715671437617067"),
1036       boost::lexical_cast<T>("56613850282803917571020710912352273128359037207464294769554425049946119446134200380023253900925711945706952706742082593051847002924694714289862350724451025928248176225776822981837"),
1037       boost::lexical_cast<T>("91603133991574585233562363299442611958170273406410496211681021886098002618016034698543374823122873780435804382549300642479384397366933102369026176290148379503036945941448260598904"),
1038       boost::lexical_cast<T>("148216984274378502804583074211794885086529310613874790981235446936044122064150235078566628724048585726142757089291383235531231400291627816658888527014599405431285122167225083580741"),
1039       boost::lexical_cast<T>("239820118265953088038145437511237497044699584020285287192916468822142124682166269777110003547171459506578561471840683878010615797658560919027914703304747784934322068108673344179645"),
1040       boost::lexical_cast<T>("388037102540331590842728511723032382131228894634160078174151915758186246746316504855676632271220045232721318561132067113541847197950188735686803230319347190365607190275898427760386"),
1041       boost::lexical_cast<T>("627857220806284678880873949234269879175928478654445365367068384580328371428482774632786635818391504739299880032972750991552462995608749654714717933624094975299929258384571771940031"),
1042       boost::lexical_cast<T>("1015894323346616269723602460957302261307157373288605443541220300338514618174799279488463268089611549972021198594104818105094310193558938390401521163943442165665536448660470199700417"),
1043       boost::lexical_cast<T>("1643751544152900948604476410191572140483085851943050808908288684918842989603282054121249903908003054711321078627077569096646773189167688045116239097567537140965465707045041971640448"),
1044       boost::lexical_cast<T>("2659645867499517218328078871148874401790243225231656252449508985257357607778081333609713171997614604683342277221182387201741083382726626435517760261510979306631002155705512171340865"),
1045       boost::lexical_cast<T>("4303397411652418166932555281340446542273329077174707061357797670176200597381363387730963075905617659394663355848259956298387856571894314480633999359078516447596467862750554142981313"),
1046       boost::lexical_cast<T>("6963043279151935385260634152489320944063572302406363313807306655433558205159444721340676247903232264078005633069442343500128939954620940916151759620589495754227470018456066314322178"),
1047       boost::lexical_cast<T>("11266440690804353552193189433829767486336901379581070375165104325609758802540808109071639323808849923472668988917702299798516796526515255396785758979668012201823937881206620457303491"),
1048       boost::lexical_cast<T>("18229483969956288937453823586319088430400473681987433688972410981043317007700252830412315571712082187550674621987144643298645736481136196312937518600257507956051407899662686771625669"),
1049       boost::lexical_cast<T>("29495924660760642489647013020148855916737375061568504064137515306653075810241060939483954895520932111023343610904846943097162533007651451709723277579925520157875345780869307228929160"),
1050       boost::lexical_cast<T>("47725408630716931427100836606467944347137848743555937753109926287696392817941313769896270467233014298574018232891991586395808269488787648022660796180183028113926753680531994000554829"),
1051       boost::lexical_cast<T>("77221333291477573916747849626616800263875223805124441817247441594349468628182374709380225362753946409597361843796838529492970802496439099732384073760108548271802099461401301229483989"),
1052       boost::lexical_cast<T>("124946741922194505343848686233084744611013072548680379570357367882045861446123688479276495829986960708171380076688830115888779071985226747755044869940291576385728853141933295230038818"),
1053       boost::lexical_cast<T>("202168075213672079260596535859701544874888296353804821387604809476395330074306063188656721192740907117768741920485668645381749874481665847487428943700400124657530952603334596459522807"),
1054       boost::lexical_cast<T>("327114817135866584604445222092786289485901368902485200957962177358441191520429751667933217022727867825940121997174498761270528946466892595242473813640691701043259805745267891689561625"),
1055       boost::lexical_cast<T>("529282892349538663865041757952487834360789665256290022345566986834836521594735814856589938215468774943708863917660167406652278820948558442729902757341091825700790758348602488149084432"),
1056       boost::lexical_cast<T>("856397709485405248469486980045274123846691034158775223303529164193277713115165566524523155238196642769648985914834666167922807767415451037972376570981783526744050564093870379838646057"),
1057       boost::lexical_cast<T>("1385680601834943912334528737997761958207480699415065245649096151028114234709901381381113093453665417713357849832494833574575086588364009480702279328322875352444841322442472867987730489"),
1058       boost::lexical_cast<T>("2242078311320349160804015718043036082054171733573840468952625315221391947825066947905636248691862060483006835747329499742497894355779460518674655899304658879188891886536343247826376546"),
1059       boost::lexical_cast<T>("3627758913155293073138544456040798040261652432988905714601721466249506182534968329286749342145527478196364685579824333317072980944143469999376935227627534231633733208978816115814107035"),
1060       boost::lexical_cast<T>("5869837224475642233942560174083834122315824166562746183554346781470898130360035277192385590837389538679371521327153833059570875299922930518051591126932193110822625095515159363640483581"),
1061       boost::lexical_cast<T>("9497596137630935307081104630124632162577476599551651898156068247720404312895003606479134932982917016875736206906978166376643856244066400517428526354559727342456358304493975479454590616"),
1062       boost::lexical_cast<T>("15367433362106577541023664804208466284893300766114398081710415029191302443255038883671520523820306555555107728234131999436214731543989331035480117481491920453278983400009134843095074197"),
1063       boost::lexical_cast<T>("24865029499737512848104769434333098447470777365666049979866483276911706756150042490150655456803223572430843935141110165812858587788055731552908643836051647795735341704503110322549664813"),
1064       boost::lexical_cast<T>("40232462861844090389128434238541564732364078131780448061576898306103009199405081373822175980623530127985951663375242165249073319332045062588388761317543568249014325104512245165644739010"),
1065       boost::lexical_cast<T>("65097492361581603237233203672874663179834855497446498041443381583014715955555123863972831437426753700416795598516352331061931907120100794141297405153595216044749666809015355488194403823"),
1066       boost::lexical_cast<T>("105329955223425693626361637911416227912198933629226946103020279889117725154960205237795007418050283828402747261891594496311005226452145856729686166471138784293763991913527600653839142833"),
1067       boost::lexical_cast<T>("170427447585007296863594841584290891092033789126673444144463661472132441110515329101767838855477037528819542860407946827372937133572246650870983571624734000338513658722542956142033546656"),
1068       boost::lexical_cast<T>("275757402808432990489956479495707119004232722755900390247483941361250166265475534339562846273527321357222290122299541323683942360024392507600669738095872784632277650636070556795872689489"),
1069       boost::lexical_cast<T>("446184850393440287353551321079998010096266511882573834391947602833382607375990863441330685129004358886041832982707488151056879493596639158471653309720606784970791309358613512937906236145"),
1070       boost::lexical_cast<T>("721942253201873277843507800575705129100499234638474224639431544194632773641466397780893531402531680243264123105007029474740821853621031666072323047816479569603068959994684069733778925634"),
1071       boost::lexical_cast<T>("1168127103595313565197059121655703139196765746521048059031379147028015381017457261222224216531536039129305956087714517625797701347217670824543976357537086354573860269353297582671685161779"),
1072       boost::lexical_cast<T>("1890069356797186843040566922231408268297264981159522283670810691222648154658923659003117747934067719372570079192721547100538523200838702490616299405353565924176929229347981652405464087413"),
1073       boost::lexical_cast<T>("3058196460392500408237626043887111407494030727680570342702189838250663535676380920225341964465603758501876035280436064726336224548056373315160275762890652278750789498701279235077149249192"),
1074       boost::lexical_cast<T>("4948265817189687251278192966118519675791295708840092626373000529473311690335304579228459712399671477874446114473157611826874747748895075805776575168244218202927718728049260887482613336605"),
1075       boost::lexical_cast<T>("8006462277582187659515819010005631083285326436520662969075190367723975226011685499453801676865275236376322149753593676553210972296951449120936850931134870481678508226750540122559762585797"),
1076       boost::lexical_cast<T>("12954728094771874910794011976124150759076622145360755595448190897197286916346990078682261389264946714250768264226751288380085720045846524926713426099379088684606226954799801010042375922402"),
1077       boost::lexical_cast<T>("20961190372354062570309830986129781842361948581881418564523381264921262142358675578136063066130221950627090413980344964933296692342797974047650277030513959166284735181550341132602138508199"),
1078       boost::lexical_cast<T>("33915918467125937481103842962253932601438570727242174159971572162118549058705665656818324455395168664877858678207096253313382412388644498974363703129893047850890962136350142142644514430601"),
1079       boost::lexical_cast<T>("54877108839480000051413673948383714443800519309123592724494953427039811201064341234954387521525390615504949092187441218246679104731442473022013980160407007017175697317900483275246652938800"),
1080       boost::lexical_cast<T>("88793027306605937532517516910637647045239090036365766884466525589158360259770006891772711976920559280382807770394537471560061517120086971996377683290300054868066659454250625417891167369401"),
1081       boost::lexical_cast<T>("143670136146085937583931190859021361489039609345489359608961479016198171460834348126727099498445949895887756862581978689806740621851529445018391663450707061885242356772151108693137820308201"),
1082       boost::lexical_cast<T>("232463163452691875116448707769659008534278699381855126493428004605356531720604355018499811475366509176270564632976516161366802138971616417014769346741007116753309016226401734111028987677602"),
1083       boost::lexical_cast<T>("376133299598777812700379898628680370023318308727344486102389483621554703181438703145226910973812459072158321495558494851173542760823145862033161010191714178638551372998552842804166807985803"),
1084       boost::lexical_cast<T>("608596463051469687816828606398339378557597008109199612595817488226911234902043058163726722449178968248428886128535011012540344899794762279047930356932721295391860389224954576915195795663405"),
1085       boost::lexical_cast<T>("984729762650247500517208505027019748580915316836544098698206971848465938083481761308953633422991427320587207624093505863713887660617908141081091367124435474030411762223507419719362603649208"),
1086       boost::lexical_cast<T>("1593326225701717188334037111425359127138512324945743711294024460075377172985524819472680355872170395569016093752628516876254232560412670420129021724057156769422272151448461996634558399312613"),
1087       boost::lexical_cast<T>("2578055988351964688851245616452378875719427641782287809992231431923843111069006580781633989295161822889603301376722022739968120221030578561210113091181592243452683913671969416353921002961821"),
1088       boost::lexical_cast<T>("4171382214053681877185282727877738002857939966728031521286255891999220284054531400254314345167332218458619395129350539616222352781443248981339134815238749012874956065120431412988479402274434"),
1089       boost::lexical_cast<T>("6749438202405646566036528344330116878577367608510319331278487323923063395123537981035948334462494041348222696506072562356190473002473827542549247906420341256327639978792400829342400405236255"),
1090       boost::lexical_cast<T>("10920820416459328443221811072207854881435307575238350852564743215922283679178069381290262679629826259806842091635423101972412825783917076523888382721659090269202596043912832242330879807510689"),
1091       boost::lexical_cast<T>("17670258618864975009258339416537971760012675183748670183843230539845347074301607362326211014092320301155064788141495664328603298786390904066437630628079431525530236022705233071673280212746944"),
1092       boost::lexical_cast<T>("28591079035324303452480150488745826641447982758987021036407973755767630753479676743616473693722146560961906879776918766301016124570307980590326013349738521794732832066618065314004160020257633"),
1093       boost::lexical_cast<T>("46261337654189278461738489905283798401460657942735691220251204295612977827781284105942684707814466862116971667918414430629619423356698884656763643977817953320263068089323298385677440233004577"),
1094       boost::lexical_cast<T>("74852416689513581914218640394029625042908640701722712256659178051380608581260960849559158401536613423078878547695333196930635547927006865247089657327556475114995900155941363699681600253262210"),
1095       boost::lexical_cast<T>("121113754343702860375957130299313423444369298644458403476910382346993586409042244955501843109351080285195850215613747627560254971283705749903853301305374428435258968245264662085359040486266787"),
1096       boost::lexical_cast<T>("195966171033216442290175770693343048487277939346181115733569560398374194990303205805061001510887693708274728763309080824490890519210712615150942958632930903550254868401206025785040640739528997"),
1097       boost::lexical_cast<T>("317079925376919302666132900992656471931647237990639519210479942745367781399345450760562844620238773993470578978922828452051145490494418365054796259938305331985513836646470687870399681225795784"),
1098       boost::lexical_cast<T>("513046096410135744956308671685999520418925177336820634944049503143741976389648656565623846131126467701745307742231909276542036009705130980205739218571236235535768705047676713655440321965324781"),
1099       boost::lexical_cast<T>("830126021787055047622441572678655992350572415327460154154529445889109757788994107326186690751365241695215886721154737728593181500199549345260535478509541567521282541694147401525840003191120565"),
1100       boost::lexical_cast<T>("1343172118197190792578750244364655512769497592664280789098578949032851734178642763891810536882491709396961194463386647005135217509904680325466274697080777803057051246741824115181280325156445346"),
1101       boost::lexical_cast<T>("2173298139984245840201191817043311505120070007991740943253108394921961491967636871217997227633856951092177081184541384733728399010104229670726810175590319370578333788435971516707120328347565911"),
1102       boost::lexical_cast<T>("3516470258181436632779942061407967017889567600656021732351687343954813226146279635109807764516348660489138275647928031738863616520008909996193084872671097173635385035177795631888400653504011257"),
1103       boost::lexical_cast<T>("5689768398165682472981133878451278523009637608647762675604795738876774718113916506327804992150205611581315356832469416472592015530113139666919895048261416544213718823613767148595520981851577168"),
1104       boost::lexical_cast<T>("9206238656347119105761075939859245540899205209303784407956483082831587944260196141437612756666554272070453632480397448211455632050122049663112979920932513717849103858791562780483921635355588425"),
1105       boost::lexical_cast<T>("14896007054512801578742209818310524063908842817951547083561278821708362662374112647765417748816759883651768989312866864684047647580235189330032874969193930262062822682405329929079442617207165593"),
1106       boost::lexical_cast<T>("24102245710859920684503285758169769604808048027255331491517761904539950606634308789203030505483314155722222621793264312895503279630357238993145854890126443979911926541196892709563364252562754018"),
1107       boost::lexical_cast<T>("38998252765372722263245495576480293668716890845206878575079040726248313269008421436968448254300074039373991611106131177579550927210592428323178729859320374241974749223602222638642806869769919611"),
1108       boost::lexical_cast<T>("63100498476232642947748781334650063273524938872462210066596802630788263875642730226171478759783388195096214232899395490475054206840949667316324584749446818221886675764799115348206171122332673629"),
1109       boost::lexical_cast<T>("102098751241605365210994276911130356942241829717669088641675843357036577144651151663139927014083462234470205844005526668054605134051542095639503314608767192463861424988401337986848977992102593240"),
1110       boost::lexical_cast<T>("165199249717838008158743058245780420215766768590131298708272645987824841020293881889311405773866850429566420076904922158529659340892491762955827899358214010685748100753200453335055149114435266869"),
1111       boost::lexical_cast<T>("267298000959443373369737335156910777158008598307800387349948489344861418164945033552451332787950312664036625920910448826584264474944033858595331213966981203149609525741601791321904127106537860109"),
1112       boost::lexical_cast<T>("432497250677281381528480393402691197373775366897931686058221135332686259185238915441762738561817163093603045997815370985113923815836525621551159113325195213835357626494802244656959276220973126978"),
1113       boost::lexical_cast<T>("699795251636724754898217728559601974531783965205732073408169624677547677350183948994214071349767475757639671918725819811698188290780559480146490327292176416984967152236404035978863403327510987087"),
1114       boost::lexical_cast<T>("1132292502314006136426698121962293171905559332103663759466390760010233936535422864435976809911584638851242717916541190796812112106617085101697649440617371630820324778731206280635822679548484114065"),
1115       boost::lexical_cast<T>("1832087753950730891324915850521895146437343297309395832874560384687781613885606813430190881261352114608882389835267010608510300397397644581844139767909548047805291930967610316614686082875995101152"),
1116       boost::lexical_cast<T>("2964380256264737027751613972484188318342902629413059592340951144698015550421029677866167691172936753460125107751808201405322412504014729683541789208526919678625616709698816597250508762424479215217"),
1117       boost::lexical_cast<T>("4796468010215467919076529823006083464780245926722455425215511529385797164306636491296358572434288868069007497587075212013832712901412374265385928976436467726430908640666426913865194845300474316369"),
1118       boost::lexical_cast<T>("7760848266480204946828143795490271783123148556135515017556462674083812714727666169162526263607225621529132605338883413419155125405427103948927718184963387405056525350365243511115703607724953531586"),
1119       boost::lexical_cast<T>("12557316276695672865904673618496355247903394482857970442771974203469609879034302660458884836041514489598140102925958625432987838306839478214313647161399855131487433991031670424980898453025427847955"),
1120       boost::lexical_cast<T>("20318164543175877812732817413986627031026543038993485460328436877553422593761968829621411099648740111127272708264842038852142963712266582163241365346363242536543959341396913936096602060750381379541"),
1121       boost::lexical_cast<T>("32875480819871550678637491032482982278929937521851455903100411081023032472796271490080295935690254600725412811190800664285130802019106060377555012507763097668031393332428584361077500513775809227496"),
1122       boost::lexical_cast<T>("53193645363047428491370308446469609309956480560844941363428847958576455066558240319701707035338994711852685519455642703137273765731372642540796377854126340204575352673825498297174102574526190607037"),
1123       boost::lexical_cast<T>("86069126182918979170007799478952591588886418082696397266529259039599487539354511809782002971029249312578098330646443367422404567750478702918351390361889437872606746006254082658251603088301999834533"),
1124       boost::lexical_cast<T>("139262771545966407661378107925422200898842898643541338629958106998175942605912752129483710006368244024430783850102086070559678333481851345459147768216015778077182098680079580955425705662828190441570"),
1125       boost::lexical_cast<T>("225331897728885386831385907404374792487729316726237735896487366037775430145267263939265712977397493337008882180748529437982082901232330048377499158577905215949788844686333663613677308751130190276103"),
1126       boost::lexical_cast<T>("364594669274851794492764015329796993386572215369779074526445473035951372751180016068749422983765737361439666030850615508541761234714181393836646926793920994026970943366413244569103014413958380717673"),
1127       boost::lexical_cast<T>("589926567003737181324149922734171785874301532096016810422932839073726802896447280008015135961163230698448548211599144946523844135946511442214146085371826209976759788052746908182780323165088570993776"),
1128       boost::lexical_cast<T>("954521236278588975816913938063968779260873747465795884949378312109678175647627296076764558944928968059888214242449760455065605370660692836050793012165747204003730731419160152751883337579046951711449"),
1129       boost::lexical_cast<T>("1544447803282326157141063860798140565135175279561812695372311151183404978544074576084779694906092198758336762454048905401589449506607204278264939097537573413980490519471907060934663660744135522705225"),
1130       boost::lexical_cast<T>("2498969039560915132957977798862109344396049027027608580321689463293083154191701872161544253851021166818224976696498665856655054877267897114315732109703320617984221250891067213686546998323182474416674"),
1131       boost::lexical_cast<T>("4043416842843241290099041659660249909531224306589421275694000614476488132735776448246323948757113365576561739150547571258244504383875101392580671207240894031964711770362974274621210659067317997121899"),
1132       boost::lexical_cast<T>("6542385882404156423057019458522359253927273333617029856015690077769571286927478320407868202608134532394786715847046237114899559261142998506896403316944214649948933021254041488307757657390500471538573"),
1133       boost::lexical_cast<T>("10585802725247397713156061118182609163458497640206451131709690692246059419663254768654192151365247897971348454997593808373144063645018099899477074524185108681913644791617015762928968316457818468660472"),
1134       boost::lexical_cast<T>("17128188607651554136213080576704968417385770973823480987725380770015630706590733089062060353973382430366135170844640045488043622906161098406373477841129323331862577812871057251236725973848318940199045"),
1135       boost::lexical_cast<T>("27713991332898951849369141694887577580844268614029932119435071462261690126253987857716252505338630328337483625842233853861187686551179198305850552365314432013776222604488073014165694290306137408859517"),
1136       boost::lexical_cast<T>("44842179940550505985582222271592545998230039587853413107160452232277320832844720946778312859312012758703618796686873899349231309457340296712224030206443755345638800417359130265402420264154456349058562"),
1137       boost::lexical_cast<T>("72556171273449457834951363966480123579074308201883345226595523694539010959098708804494565364650643087041102422529107753210418996008519495018074582571758187359415023021847203279568114554460593757918079"),
1138       boost::lexical_cast<T>("117398351213999963820533586238072669577304347789736758333755975926816331791943429751272878223962655845744721219215981652559650305465859791730298612778201942705053823439206333544970534818615050106976641"),
1139       boost::lexical_cast<T>("189954522487449421655484950204552793156378655991620103560351499621355342751042138555767443588613298932785823641745089405770069301474379286748373195349960130064468846461053536824538649373075643864894720"),
1140       boost::lexical_cast<T>("307352873701449385476018536442625462733683003781356861894107475548171674542985568307040321812575954778530544860961071058329719606940239078478671808128162072769522669900259870369509184191690693971871361"),
1141       boost::lexical_cast<T>("497307396188898807131503486647178255890061659772976965454458975169527017294027706862807765401189253711316368502706160464099788908414618365227045003478122202833991516361313407194047833564766337836766081"),
1142       boost::lexical_cast<T>("804660269890348192607522023089803718623744663554333827348566450717698691837013275169848087213765208489846913363667231522429508515354857443705716811606284275603514186261573277563557017756457031808637442"),
1143       boost::lexical_cast<T>("1301967666079246999739025509736981974513806323327310792803025425887225709131040982032655852614954462201163281866373391986529297423769475808932761815084406478437505702622886684757604851321223369645403523"),
1144       boost::lexical_cast<T>("2106627935969595192346547532826785693137550986881644620151591876604924400968054257202503939828719670691010195230040623508958805939124333252638478626690690754041019888884459962321161869077680401454040965"),
1145       boost::lexical_cast<T>("3408595602048842192085573042563767667651357310208955412954617302492150110099095239235159792443674132892173477096414015495488103362893809061571240441775097232478525591507346647078766720398903771099444488"),
1146       boost::lexical_cast<T>("5515223538018437384432120575390553360788908297090600033106209179097074511067149496437663732272393803583183672326454639004446909302018142314209719068465787986519545480391806609399928589476584172553485453"),
1147       boost::lexical_cast<T>("8923819140067279576517693617954321028440265607299555446060826481589224621166244735672823524716067936475357149422868654499935012664911951375780959510240885218998071071899153256478695309875487943652929941"),
1148       boost::lexical_cast<T>("14439042678085716960949814193344874389229173904390155479167035660686299132233394232110487256988461740058540821749323293504381921966930093689990678578706673205517616552290959865878623899352072116206415394"),
1149       boost::lexical_cast<T>("23362861818152996537467507811299195417669439511689710925227862142275523753399638967783310781704529676533897971172191948004316934631842045065771638088947558424515687624190113122357319209227560059859345335"),
1150       boost::lexical_cast<T>("37801904496238713498417322004644069806898613416079866404394897802961822885633033199893798038692991416592438792921515241508698856598772138755762316667654231630033304176481072988235943108579632176065760729"),
1151       boost::lexical_cast<T>("61164766314391710035884829815943265224568052927769577329622759945237346639032672167677108820397521093126336764093707189513015791230614183821533954756601790054548991800671186110593262317807192235925106064"),
1152       boost::lexical_cast<T>("98966670810630423534302151820587335031466666343849443734017657748199169524665705367570906859090512509718775557015222431021714647829386322577296271424256021684582295977152259098829205426386824411990866793"),
1153       boost::lexical_cast<T>("160131437125022133570186981636530600256034719271619021063640417693436516163698377535248015679488033602845112321108929620534730439060000506398830226180857811739131287777823445209422467744194016647915972857"),
1154       boost::lexical_cast<T>("259098107935652557104489133457117935287501385615468464797658075441635685688364082902818922538578546112563887878124152051556445086889386828976126497605113833423713583754975704308251673170580841059906839650"),
1155       boost::lexical_cast<T>("419229545060674690674676115093648535543536104887087485861298493135072201852062460438066938218066579715409000199233081672091175525949387335374956723785971645162844871532799149517674140914774857707822812507"),
1156       boost::lexical_cast<T>("678327652996327247779165248550766470831037490502555950658956568576707887540426543340885860756645125827972888077357233723647620612838774164351083221391085478586558455287774853825925814085355698767729652157"),
1157       boost::lexical_cast<T>("1097557198057001938453841363644415006374573595389643436520255061711780089392489003778952798974711705543381888276590315395738796138788161499726039945177057123749403326820574003343599955000130556475552464664"),
1158       boost::lexical_cast<T>("1775884851053329186233006612195181477205611085892199387179211630288487976932915547119838659731356831371354776353947549119386416751626935664077123166568142602335961782108348857169525769085486255243282116821"),
1159       boost::lexical_cast<T>("2873442049110331124686847975839596483580184681281842823699466692000268066325404550898791458706068536914736664630537864515125212890415097163803163111745199726085365108928922860513125724085616811718834581485"),
1160       boost::lexical_cast<T>("4649326900163660310919854588034777960785795767174042210878678322288756043258320098018630118437425368286091440984485413634511629642042032827880286278313342328421326891037271717682651493171103066962116698306"),
1161       boost::lexical_cast<T>("7522768949273991435606702563874374444365980448455885034578145014289024109583724648917421577143493905200828105615023278149636842532457129991683449390058542054506691999966194578195777217256719878680951279791"),
1162       boost::lexical_cast<T>("12172095849437651746526557151909152405151776215629927245456823336577780152842044746936051695580919273486919546599508691784148472174499162819563735668371884382928018891003466295878428710427822945643067978097"),
1163       boost::lexical_cast<T>("19694864798711643182133259715783526849517756664085812280034968350866804262425769395853473272724413178687747652214531969933785314706956292811247185058430426437434710890969660874074205927684542824324019257888"),
1164       boost::lexical_cast<T>("31866960648149294928659816867692679254669532879715739525491791687444584415267814142789524968305332452174667198814040661717933786881455455630810920726802310820362729781973127169952634638112365769967087235985"),
1165       boost::lexical_cast<T>("51561825446860938110793076583476206104187289543801551805526760038311388677693583538642998241029745630862414851028572631651719101588411748442058105785232737257797440672942788044026840565796908594291106493873"),
1166       boost::lexical_cast<T>("83428786095010233039452893451168885358856822423517291331018551725755973092961397681432523209335078083037082049842613293369652888469867204072869026512035048078160170454915915213979475203909274364258193729858"),
1167       boost::lexical_cast<T>("134990611541871171150245970034645091463044111967318843136545311764067361770654981220075521450364823713899496900871185925021371990058278952514927132297267785335957611127858703258006315769706182958549300223731"),
1168       boost::lexical_cast<T>("218419397636881404189698863485813976821900934390836134467563863489823334863616378901508044659699901796936578950713799218391024878528146156587796158809302833414117781582774618471985790973615457322807493953589"),
1169       boost::lexical_cast<T>("353410009178752575339944833520459068284945046358154977604109175253890696634271360121583566110064725510836075851584985143412396868586425109102723291106570618750075392710633321729992106743321640281356794177320"),
1170       boost::lexical_cast<T>("571829406815633979529643697006273045106845980748991112071673038743714031497887739023091610769764627307772654802298784361803421747114571265690519449915873452164193174293407940201977897716937097604164288130909"),
1171       boost::lexical_cast<T>("925239415994386554869588530526732113391791027107146089675782213997604728132159099144675176879829352818608730653883769505215818615700996374793242741022444070914268567004041261931970004460258737885521082308229"),
1172       boost::lexical_cast<T>("1497068822810020534399232227533005158498637007856137201747455252741318759630046838167766787649593980126381385456182553867019240362815567640483762190938317523078461741297449202133947902177195835489685370439138"),
1173       boost::lexical_cast<T>("2422308238804407089268820758059737271890428034963283291423237466738923487762205937312441964529423332944990116110066323372235058978516564015277004931960761593992730308301490464065917906637454573375206452747367"),
1174       boost::lexical_cast<T>("3919377061614427623668052985592742430389065042819420493170692719480242247392252775480208752179017313071371501566248877239254299341332131655760767122899079117071192049598939666199865808814650408864891823186505"),
1175       boost::lexical_cast<T>("6341685300418834712936873743652479702279493077782703784593930186219165735154458712792650716708440646016361617676315200611489358319848695671037772054859840711063922357900430130265783715452104982240098275933872"),
1176       boost::lexical_cast<T>("10261062362033262336604926729245222132668558120602124277764622905699407982546711488272859468887457959087733119242564077850743657661180827326798539177758919828135114407499369796465649524266755391104990099120377"),
1177       boost::lexical_cast<T>("16602747662452097049541800472897701834948051198384828062358553091918573717701170201065510185595898605104094736918879278462233015981029522997836311232618760539199036765399799926731433239718860373345088375054249"),
1178       boost::lexical_cast<T>("26863810024485359386146727202142923967616609318986952340123175997617981700247881689338369654483356564191827856161443356312976673642210350324634850410377680367334151172899169723197082763985615764450078474174626"),
1179       boost::lexical_cast<T>("43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"),
1180       boost::lexical_cast<T>("70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501")
1181    };
1182    static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0]));
1183
1184    return data;
1185 }
1186
1187 template <class T>
1188 std::vector<std::pair<T, T> > const& fibonacci_numbers_permution_1()
1189 {
1190    typedef boost::mpl::int_<
1191       ((std::numeric_limits<T>::digits <= 16) ? 16 : ((std::numeric_limits<T>::digits <= 32) ? 32 : (std::numeric_limits<T>::digits <= 64) ? 64 : 0))
1192    > tag_type;
1193
1194    static std::vector<std::pair<T, T> > data;
1195    static bool init = false;
1196    if(!init)
1197    {
1198       init = true;
1199       for(unsigned i = 0; i < fibonacci_numbers<T>(tag_type()).size() - 1; ++i)
1200          data.push_back(std::make_pair(fibonacci_numbers<T>(tag_type())[i], fibonacci_numbers<T>(tag_type())[i + 1]));
1201    }
1202    return data;
1203 }
1204
1205 template <class T>
1206 std::vector<std::pair<T, T> > const& fibonacci_numbers_permution_2()
1207 {
1208    typedef boost::mpl::int_<
1209       ((std::numeric_limits<T>::digits <= 16) ? 16 : ((std::numeric_limits<T>::digits <= 32) ? 32 : (std::numeric_limits<T>::digits <= 64) ? 64 : 0))
1210    > tag_type;
1211
1212    static std::vector<std::pair<T, T> > data;
1213    static bool init = false;
1214    if(!init)
1215    {
1216       init = true;
1217       for(unsigned i = 0; i < fibonacci_numbers<T>(tag_type()).size(); ++i)
1218          for(unsigned j = 0; j < fibonacci_numbers<T>(tag_type()).size(); ++j)
1219             data.push_back(std::make_pair(fibonacci_numbers<T>(tag_type())[i], fibonacci_numbers<T>(tag_type())[j]));
1220    }
1221    return data;
1222 }
1223
1224 template <class T>
1225 std::vector<std::pair<T, T> > const & trivial_gcd_test_cases()
1226 {
1227    static const std::pair<T, T> a[] = {
1228       std::pair<T, T>(0, 0),
1229       std::pair<T, T>(0, 832040u),
1230       std::pair<T, T>(832040u, 0),
1231       std::pair<T, T>(1u << 15, 1u << 4),
1232       std::pair<T, T>(1u << 3, 1u << 14),
1233       std::pair<T, T>(832040u, 832040u),
1234       std::pair<T, T>(991u * 3 * 7, 991u),
1235       std::pair<T, T>(991u * 2, 991u),
1236    };
1237    static const std::vector<std::pair<T, T> > data(a, a + sizeof(a) / sizeof(a[0]));
1238    return data;
1239 }
1240